FamilyMusical comedian Tim Minchin met his wife when he was only 17 – they've been together 19 years. When he became a father, he discovered a whole new world of feeling to inspire his songs about the ups and downs of family life

More than 100,000 people saw Tim Minchin's latest show. He's sold out the O2 in London and won strings of comedy and music awards. But, on the quiet, this father of two under-fives also happens to be the king of ambivalent (and honest) parenting. His anarchic songs talk about the highs and lows of family life. But mostly the lows. This is from his song Lullaby, sung as if by a desperate dad in the small hours: "Where is the line between patting and hitting? When is rocking rocking? And when is it shaking? I don't know what else I can do to try and hush you. My heart says, 'I love you'. But my brain's saying, 'Fuck you.'"

This month sees the transfer to the West End of his latest baby, the Royal Shakespeare Company's Matilda, for which Minchin, 36, has just been shortlisted for a British Composer Award 2011. He looks like a Gothic Fraggle and bounces around like a little boy, his huge eyes boggling.

"Roald Dahl altered my childhood – by a long shot. He was a standard part of the culture [in Australia]. The BFG was huge for me, and George's Marvellous Medicine and Danny, Champion of the World. I was 13 when Matilda came out, so I wasn't reading Dahl by then. But in the early 1980s I loved him. I had a penchant for being a bit naughty and he felt a bit naughty. I even tried to write like him and got into trouble for putting naughty words in my stories," he says.

Usually described as "British-Australian", Minchin was born in Northampton in 1975 but by the following year he was already back in his parents' native Perth. He describes himself as very much an Australian, although he is now based in north London with his wife, Sarah, 38, their daughter Violet, five, and son Caspar, two. While he does sing mostly about blow-up dolls and atheism, a lot of the softer moments in his songs come from how much he misses his family back home – and how life as a father, raising his family away from his own parents, has affected him.

One of four siblings, his elder brother and two younger sisters all live in Australia, as do his parents, Dave, a surgeon, and mum Ros. (Minchin was born while his father was on a fellowship at the Royal College of General Practitioners in Northampton.) One of his best-known songs, White Wine in the Sun, addressed to his daughter, is about the moment you realise the connection between the generations: "You will learn some day that wherever you are and whatever you face, these are the people who make you feel safe in this world, my sweet blue-eyed girl."

He is proud to have been raised in a household where the parents were "just strict enough". "My mum didn't brook emotion. It's very easy to paint your parents as two-dimensional and of course my mum obsessively loved us. But she'd also say, 'Don't be so pathetic.' So it felt like, 'Don't wallow.' On the other hand, I tell my kids I love them all the time. I don't think you should bring up your kids with no wallowing. Somewhere in there is an area where you make sure your kids are all right but they can also cry. Just maybe not every morning." (Which is, unfortunately, what Violet is doing at school every day at the moment. "She has spent so much time with us because we tour so much and hasn't had a lot of socialisation. So she'll say, 'I don't want to leave you and I want to be able to talk to you when I want to.' There is a point where you have to go, 'OK, we're not going to go through this for hours.'")

As a child he messed around a lot and had no idea what he would do with his life. "My brother and I played music together and we all liked to show off. But I wasn't a particularly musical kid. I did piano lessons and quit. I got kicked out of the choir. I threw a lot of basketballs into hoops and played the piano, all just to avoid going into my bedroom and doing my homework. I wanted to write songs for theatre, I wanted to act, I wanted to play in bands. But I never specialised, even when my mum said, "You need to get a teaching degree as a fallback." I didn't find comedy until I was 28."

His parents worried he would never make a living. "We argued for 12 solid years about me not working hard enough. That was very painful. But at the time I took education for granted in the way you do when you go to a private school for 11 years. I knew I was lucky – I wasn't brought up in a bubble. But I did not have a burning desire to learn." Now his parents are very proud. "They are not demonstrative, though," he says, laughing. "We are not Oprah about our relationship. We all get along, but [my parents] don't say, 'We love you, son.'"

Minchin has been with his wife, Sarah, since they were teenage sweethearts in Perth. He is excruciatingly honest about how difficult it is to be in a long-term relationship and often refers to it on stage.

"We have been together 19 years. I was 17 when I met her. Yeah, the sacrifice of not being able to shag other women is a full-on sacrifice. Because I really, really like women. And I haven't had loads of partners. So that's still really in there, that desire. But there is no way I would risk not being able to live with my kids. It's bullshit. There is no way. Lucky it was all locked in before this world [music] came to seduce me. So I'm basically un-seduceable in a really nice way. Not because I don't want to shag all these women. I desperately do. But I'm just, like, 'Look, I'd give anything to get nude with you right now. Except for what I've got. I wouldn't give that.'"

He comes across as slightly stunned by his (relatively) overnight success. He decided to make a go of comedy in 2005 when his Edinburgh fringe show was an unexpected hit. "We went back in 2006 with the intention of migrating. Sarah was wandering around London with seven months worth of foetus in her guts and I was up doing battle with Edinburgh. Suddenly everything went from us being this poor, childless, renting couple in Melbourne, me a jobbing musician, to this new life. Comedian. Baby. House. Income. London represents the idea that someone pulled away the set from my life and replaced it with another. 'Here is your new baby. Here is your new life. And now you do comedy.' Without being smug, it's the best fun. "

He would like another child but doesn't feel it's fair on his wife (who gave up her job as a social worker to be a full-time mother). "I would go again. But it's completely unfair. Because I don't have to do it all. There are no grandparents around and often Sarah will get four hours' sleep and I will be, like, 'Sorry, I've got a show tomorrow and a cold coming on and I have to sleep.' I don't feel good about that."

His goal is to write more, perhaps record an album. And keep mixing different emotions in his songs. "My daughter was two weeks old when I wrote White Wine in the Sun. I can remember just sobbing and having to leave the room. It was as if I was having to fight with my own guts. It wasn't so much that I missed my family in that clichéd sense. It was about what having a kid does to you. It gives you that feeling of [he mocks himself in a cheesy Elton John sing-song voice] 'circle of life'. And almost that caveman feeling of, 'I must take this thing to its people.'

"It's a way of saying, 'Name this. This is us. This is one of us.' That's what I love about parenting. You get this feeling towards your child of, 'Yes, I've got to give this to my mum.' You want this new thing to be a member of that scrum of emotional safety and emotional complexity." Then he remembers his parents are coming over for the opening night of Matilda. And it's on his daughter's birthday. And he's buying her a new dress. And he almost gets a bit weepy.

Tim Minchin and the Heritage Orchestra is out on DVD on 14 November. Matilda the Musical opens on 24 November, matildathemusical.com

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