Here's a quiz question: name the zombie who rescued Tina Fey from Sarah Palin. Clue: he famously earned $1 billion bringing to life exhibits in Washington's Smithsonian Institution.

To put Shawn Levy's CV like this is to mirror his skewed sense of humour. He made his acting debut playing scarily dead in a low-budget horror film, Zombie Nightmare, but perversely ended up directing family comedies, graduating from Cheaper by the Dozen and Pink Panther to the lucrative Night at the Museum franchise.

He's just helped Saturday Night Live stand-up Tina Fey shed her Sarah Palin impersonator tag by rebranding her as a romantic comedy film actress in Date Night, but is now about to switch over to drama by directing Hugh Jackman in the Steven Spielberg-produced Real Steel. "I just enjoy working in a variety of genres," he says.

Maybe his reluctance to conform to type comes from growing up in Montreal. It's hardly a coincidence that Hollywood comedy is so dominated by Canadians – Mike Myers, Jim Carrey, Bill Murray, Ivan and Jason Reitman, to mention a few.

"It's some kind of outsider perspective that allows us to see the comedy in things," he says. Much like the Irish in Britain, who seem to belong but have a foot somewhere else? "That's very much how we feel as Canadians."

Date Night is a variation on The Out-of Towners. Fey teams up with deadpan Steve Carell from The US Office and Little Miss Sunshine to play a run-of-the mill suburban New Jersey couple with two lively kids who try to escape the routine of family life by heading off to Manhattan for a night out. They poach a no-show couple's reservation at the city's hottest restaurant and get mistaken by corrupt cops for blackmailers trying to rip off a mob boss who has crooked dealings with a leading politician. It's a classic Hitchcock innocents-presumed-guilty situation but played for laughs as the couple get sucked into a helter-skelter caper of car chases, shoot-outs, lap-dancing strippers and rooftop denouements.

Levy worked on the screenplay with Fey and Carell early on. "We were just grown-ups getting together telling stories about our marriages. I pillaged stuff that came up and put it in the film." The idea of stealing a table in a crowded restaurant came from Levy's attempt to sneak into first-class on a plane. "I got the champagne. Life was fabulous for three minutes. Then the proper people appeared. I was booted back to economy."

Although the script was meticulously worked out, much of it is improvised. "When we started shooting I'd do two or three takes as scripted and say, 'OK, anyone got any ideas?' We then improvised an additional few takes. That gave me lots of freedom and choice in the editing room."

As a teenager Levy was drawn to drama rather than comedy. "My favourite movies tended to be dramas like Gallipoli, Jerry Maguire, The Shawshank Redemption or Good Will Hunting. Other than the John Hughes movies, I don't think any of my top 20 movies were comedies. I didn't even know that I was funny until my mid-20s. And then I found it came naturally to me as a director. What I found funny tended to sync up with what audiences found funny."

After the huge success of the Night at the Museum films he can now do whatever he likes. "Once you've made $1bn for a studio, it's very liberating. If you walk in like I did and say, 'I want to make a movie about marriage; it's going to have action, it's going to have comedy, it's going to be relatable to ordinary life; it's called Date Night', they just say yes."

So when Steven Spielberg asked him to direct Real Steel, a sci-fi story about a future in which people are bored with human boxing, so robots battle each other, Levy was able to set his own terms. "I told Steven you can't do a movie just about robots in 2011. Other than Wall-E I haven't seen any movie about machines that's genuinely moving. If I'm going to direct it's going to be a very emotional father/son drama with shades of ET and shades of Rocky."

He's also working with Tom Cruise and Ben Stiller to follow up their Tropic Thunder success with The Hardy Men, based on the famous boys' detective stories.

"Now grown-up, the boys resent being famous so young. They've issues with each other and their dad. It becomes a kind of metaphor for what happens when you peak at 16 and your whole life will never be as golden as it once was. We'll make it if we can get a script all three of us love – and if all three of us are available."

Date Night opens on Friday