Chiara Mastroianni: I only saw my parents together on screen

When you've grown up as the daughter of not one but two screen icons, you might be fed up with talking about how great your parents are. Especially when you're in the same business. Not so with Chiara Mastroianni. "I hate talking about myself," the actor tells me very early into our interview. "So, you know, I can just bury all that quite easily. If someone wants to know about my mother and father, I tell them – everyone thinks they know them better than I do anyway."

In mainland Europe that may be true, though they are perhaps less revered in modern-day Britain. Mastroianni's parents are Catherine Deneuve, still the grande dame of the French screen, and the late Marcello Mastroianni, Italy's most famous and prolific film star and the man who for many defined 1960s cool with his role in La Dolce Vita.

They become the golden couple of European cinema in the early 1970s when they embarked on a four-year love affair and made five films together, none of them particular classics but all of them daring, experimental and, at the time, oh-so-very-European, dealing with sex and sexual politics for directors such as Marco Ferreri and Jacques Demy. Chiara was born in 1972, when her father was 50 and her mother had already been married to David Bailey, after having a son with Roger Vadim – the former lover of Brigitte Bardot – following a brief relationship. "I've never seen my parents together, never in my whole life" she says. "They split when I was two, so I've no recollection of them as a couple. I've never even seen them kiss – except in the movies."

One of the first films she ever saw was Jacques Demy's comedy A Slightly Pregnant Man, in which her parents starred as an ordinary couple until the husband is declared pregnant and becomes an international medical sensation. "Imagine, you've never seen your parents together but then you see them doing this? It's not even a very good movie, but it made quite an impression on me, I can tell you. That's where my life gets really psychedelic. You know, I don't need hallucinogenics: my genes make their own acid."

Far from shying away from such illustrious antecedents, Mastroianni appears to embrace them. Last month she came to the UK to promote the latest film in which she stars with her mother, Christophe Honoré's rather mannered modern musical Beloved, which itself pays obvious homage to the great Deneuve musicals of yore such as The Umbrellas of Cherbourg and Les Demoiselles de Rochefort. Mastroianni previously appeared with her mother in André Téchiné's 1993 film Ma Saison Préférée, Iranian director Marjane Satrapi's 2007 cartoon memoir Persepolis (in voiceover), and Arnaud Desplechin's family saga A Christmas Tale, from 2008. Each time, Mastroianni has re-enforced the offscreen family tie by playing her mother's on-screen daughter (daughter-in-law in the latter).

"I guess if she wasn't my mother I might be scared of working with her," says Mastroianni. "But the relationships we play on screen are nothing like the one we have in real life. That would be stupid. And pointless – what would be the fun in creating something the same as real life? My real relationship with my mother is so intimate that it never resembles something you put on screen. For example, people often think my mother is cold; she is not. She is cautious and she is very funny, but she takes time for you to be able to get to know her in real life and she brings that to her characters on screen. She is secret and shy but she is very charismatic so it's hard to see that hidden part of her, so blinding is her charisma."

In Honoré's film, Mastroianni plays the daughter of Deneuve who is married to a man in spectacles looking not unlike her father. In a typically cineaste bit of casting, this man is played by Czech director Miloš Forman. "He does look a bit like my dad and I guess that's what you're supposed to think as a viewer. Actually, Miloš and my dad both had the same appetite for food – neither of them can wait to get to the next big meal. Dad was always saying on set: 'Let's get this shot done and then we can all have cutlets.'

"When I told my mother I was going to be an actress, she was so disappointed. She freaked out. She wanted me to do something 'serious' as she calls it, to go to university and study. One day, she turned round to me and said: 'You should have been an archaeologist.' I mean, what? It's crazy. She left school very young, you see, so I think she felt protective of me. I know, she's been a very successful actress with an amazing career but she does know she's been lucky with that and that most actresses don't work so often or so long. Even then, mother is always worried there will be no next job. Can you believe that?"

Was her father equally concerned about a career in the spotlight? "Oh no, not at all. When I told him, he threw a party. It was like we ran a family restaurant and I'd just said I'd take over the business. But then he always threw a party when I was around – it was like, 'Ah tonight, you've just got here, we must have a feast', and the next night, it was like, 'You're here, let's celebrate', and then when I was going the night after that, he'd say 'Ah, you're leaving, we must mark this occasion with a dinner.'"

Oddly, Mastroianni's private life has somewhat mirrored her mother's. She has two children, Milo and Anna, by different fathers, both fairly public relationships in France, first to the sculptor and film-maker Pierre Torreton, then to the singer Benjamin Biolay. "It's true, I am a single mother," she says, "and when I was growing up there was definitely no man around. But I don't think I'm repeating patterns. I've been married and had lovely relationships with the fathers of my children, compared to the rollercoaster of my own childhood."

Was it a difficult childhood or a glamorous one? "When you're a child, you don't know either way. It's just your reality. I used to envy other kids whose parents worked in offices and came home every night for dinner, I know that. I'd miss my mother when she went away – we didn't have Skype or cellphones of course so when she was, say, filming in Africa, you couldn't get hold of her, you had to wait until she was back at the hotel and hope she would answer the phone. I remember those hours of waiting up to talk to her and having to go to bed without saying good night. She'll tell you she wasn't away that much but I can show you her filmography to prove to you that she most definitely was."

Visiting her father in Rome was always more fun. Mastroianni recalls getting taken straight from the airport to Rome's legendary Cinecittá studios where her father would invariably be shooting. "It was much better to see him on set. If he wasn't working, he'd be miserable. I sometimes went to see him in the holidays and it was terrible. He'd just eat a lot and take long naps, but if he was part of a film, he'd be full of life.

"He didn't like private dressing rooms or anything. At Cinecittá, we would eat at this little coffee shop where everyone went for lunch and I remember sitting there and at the next table there'd be a Roman centurion and over there would be someone as Napoleon or a king, you know, from whatever films they were making at this studio. It was magic for me."

At seven years old, she turned up to the making of a Federico Fellini film, City of Women.

"I didn't know who he was, but he asked me if I wanted to be in the film with my dad. I was so excited. It was a scene on a fake train, so there were the men outside rolling the landscape so it looks like you're moving – I thought that was genius. I had to make monkey faces at my dad, but Fellini said little girls shouldn't pull faces at their real dad, so he would sit in and I had to make them at him.

"And so we did it but when it came out, this film, which is my dad surrounded by all these women, well, I wasn't allowed to see it. But I remembered it, and when I did get to see it a few year's later, well, the first thing I saw was that I was cut from the film. Cut. Fellini cut me!

"So I have never watched the rest of the film. Actually, it was a very good lesson as an actress, because until you see any film and see yourself up there, you will never ever know what the director has done with you."

Had she picked up a lot of advice and tricks of the trade over the years from her parents? "My mother and I rarely talk about the job, even when we're working together. She'd rather talk about other movies, other people's performances. Dad did like to talk about it, though. He was very honest about being an actor. He'd say: 'There are only two things to remember: try to be as natural as possible when you talk, and when you're walking across a dolly track, try and do it without looking at your feet, then you'll be fine.' And that's it – 200 movies' worth of experience in two sentences."

Although she readily admits to not having watched all her parents films (between them, they've made over 300), Mastroianni is obviously very proud of her heritage. Her favourite film her mother has been in is Roman Polanski's London-set Repulsion and of her father's films she likes Divorce Italian Style and What Time Is It?, which he made with Massimo Troisi, playing his son – "It's just so terribly sad and brilliant".

She is bright, funny and relaxed. She has a distinctive mole on the right side of her chin and she doesn't really look like her mother. Nobody does. I've had dinner with her mother before, and I can tell you, Mastroianni is certainly less guarded. "It was probably because my mother likes to smoke and at dinner you can't do that any more," says the daughter. "I'm proud of my mother because she's so independent. She never accepts anybody's demands. She's a bit of a rebel, both in reality and in the films she makes. Tristana, Belle de Jour [both directed by Luis Buñuel], these are audacious films and they're very much part of her. She had many lives before I came along and I don't want to know about all of them.

"But Dad, you know, he also did brave films like La Dolce Vita. He'd always tell me how the Catholic Italians hated it and screamed at him and threw tomatoes, but he wasn't very daring in real life. He'd shout at me for wearing makeup or getting home after midnight. And I'd think: hold on, you made La Grande Bouffe and were farting for all to see, so how can you be giving me hell for a bit of mascara? So, I think maybe you can be modern in your choices as an artist, but not always a father or a mother. But," she laughs, "me, I'm a very cool mum."

Not many children can have so much of their family to watch and treasure for years to come, no matter how many photos or home videos a family may take. "Yes," admits Mastroianni, "but it's not the same. Mother on the screen is not really her. That's what I say to my kids. But since my father died [in 1996], I'm beginning to see what a lucky thing it is to have him around still. He was one of those actors who was actually quite like his on-screen characters.

"But what really sticks is the voice. You can hear it in another room and it's like he's still there. That's what gets me after all this time – an echo."

Beloved is released on 11 May