The Miller's Tale - Rebecca Miller interview

Aidan Smith persuades the multi-talented but notoriously private Rebecca Miller to open the book just a little on life with her film star husband Daniel Day-Lewis, and her playwright father Arthur

Photograph: Fran Veale

DANIEL DAY-LEWIS has done it again. Few thought he could better Gangs Of New York, but with There Will Be Blood he's raised the bar for intensity of performance. And I'm not talking about his acting.

The much-decorated star is in a class of his own as a wife-thanker. Collecting his 2003 Best Actor Bafta for Gangs, he gazed down at the woman with the fine-boned face framed by the pre-Raphaelite curls in the seat next to the one he'd just vacated and said: "There are so many things I could say but what I am going to say is that you are simply the best sport I've ever met in my life."

This year, with the TV cameras pre-programmed to capture the blush in full, he insisted that the Bafta for Blood would not have been winnable without the assistance of "Sergeant-Major Miller". And a few weeks later at the Oscars, he addressed his better half by what we might assume he regards as her full and proper name – "the enchantingly optimistic, open-minded, beautiful, Rebecca Miller."

She sounds quite a woman, does Miller, but can you really be a sergeant-major and enchantingly anything at the same time? Assuming they are different versions of the same person, I am hoping to meet the latter in London today but am concerned that the former might show up. Miller is not known for being quite so gushy about the men in her life – either Day-Lewis or her late father, the playwright Arthur Miller.

She has a career of her own as both a film director and a writer and, perfectly understandably, would prefer to talk about that. This can cause frustration and provoke bitchiness, with the author of a Vogue profile feeling moved to complain: "She's Arthur Miller's daughter and Daniel Day-Lewis' wife, for God's sake. Why else are we here?"

In previous interviews, polite but firm warnings were issued – no, she wouldn't talk about these two colossi in her life. Then, presumably when she tired of this, Sergeant-Major Miller started delegating. I get my order to this effect from the PR.

But the welcome is friendly. In her hotel bar, Miller is dressed in cardigan, jeans and boots which are definitely more enchanting than army-issue. This encourages me to begin by asking if she's been to any great parties recently and she laughs – in an accent that's firmly Brooklyn, just like her old man's.

For Gangs, she says, the Baftas were "cool". But this year, with more pressure on the bridesmaid event because of a threat to the Oscars, the atmosphere was "fraught". "The moment-to-moment of these things isn't as much fun as you might think," says Miller, "though it's really nice when someone you know is singled out and appreciated."

Miller is very happy that that someone is Day-Lewis and not her, even though she used to be an actress and presumably sought the same approbation. She starred in the lesser works of good directors such as Mike Nichols and Alan Pakula and maybe her better-known films were Regarding Henry with Harrison Ford and Consenting Adults alongside Kevin Spacey. But she insists she was only using acting to learn about directing.

"Thank God my movies were flops," she says. "If I had become a movie star that would have been a personal disaster. Friends wondered what the hell I was doing at that time because acting seemed so out of character. But I knew I wasn't suited to it. I don't like my face being the focus."

Miller was born in 1962, the year Marilyn Monroe, her father's second wife, died. Her mother was the photographer Inge Morath, who became the third Mrs Miller after meeting Arthur on the set of The Misfits, Monroe's final film, which he'd scripted.

Before acting, Miller tried painting. Was she deliberately avoiding becoming a writer? "It's possible. But I wrote a lot when I was younger. It seems odd, given I've always written, that I didn't try to get published until I was married and had started a family." I attempt some (well-intentioned) flattery and tell her she was brave to risk comparison with the author of Death Of A Salesman, The Crucible and A View From The Bridge, whereupon she reverts to sergeant-major mode again. "Maybe this is hard for you to digest but I wasn't scared of the reaction I'd get, and I'm still not."

Miller has mislaid those early attempts at fiction but they were "very extreme, very violent". As a child she was obsessed with the devil and, as a college student, would have to complete mundane tasks within an allotted time or else risk dying before she was 36. She adds: "It didn't even occur to me that those stories would be disturbing to read. I think I write with a kind of blindness about expectation and, to me, that's a handy thing."

So what does Miller write about now she's finally in print? In the short story collection Personal Velocity and the scripts for the films Angela, Proof and The Ballad Of Jack And Rose – the latter being Day-Lewis directed by Miller – there's usually been a father and, also, a daughter. Sometimes the girl struggles to emerge from the man's shadow; other times she worries about him dying (Miller's father was 46 when she was born). Now comes her first novel The Private Lives Of Pippa Lee in which the heroine is married to a publishing giant – "the virile champion of the Great American novel" – who's 30 years her senior and fading fast.

This might seem a wacky notion, I say, but there seems to something of a theme here. Miller smiles tensely, insists her work has always been personal, and eventually offers up the odd crumb from the family table.

Her first memory of her childhood in rural Connecticut was of running into a cluster of butterflies and, because she was wearing a butterfly-patterned dress, of thinking she'd "just disappeared – it was euphoric". But she cannot remember the first time she realised her father was famous.

That Arthur Miller was a "shadow person", she says, though she does describe her family as being "like a circus". Was it glamorous? "Well, only if you consider being surrounded by intellectuals glamorous. It wasn't materialistic and it wasn't about money. In many ways it was quite spartan. If a coffee pot broke, you glued it back together."

In a house full of books she read everything – "from Tolstoy to Fear Of Flying." Did her father read her first scribbles? "Yes, but it wasn't like he got under my car to fix the oil. I learned more by example." Her favourite line of his comes from Death Of A Salesman – "Wonderful coffee… meal in itself." All the more so, presumably, when poured from a cracked pot.

The Private Lives Of Pippa Lee is very good, and very John Updike in its suburban set-up, before the sex 'n' drugs 'n' fear of death kick in – and so doesn't really need the help of fame-by-association. And before it hits the shelves, an impossibly starry cast has signed up for the film version, including Julianne Moore, Winona Ryder, Keanu Reeves, Robin Wright Penn, Monica Bellucci and Maggie Gyllenhaal. Miller will direct in New York, where she and Day-Lewis live part of the year, the rest being geared round the schooling of their two young sons in Co Wicklow in Ireland.

Would she like to make another film with her husband? "Of course". What's it like living with an actor who, legend has it, self-mutates into his characters? "You'll have to ask him." Rebecca Miller, after a few false starts, has found her voice but saves the best of it for her writing. "I've got this three-hour window after picking up the boys and I get so lost in my writing that I forget to take off my coat." She adds that her desk is entirely surrounded by an imposing moat of books, but I think I might have been able to guess that.

• The Private Lives Of Pippa Lee (Canongate) is published on April 3, price £9.99