Naomi Watts says that she lives a double life. “There have been times when my kids see a photo or a flash of us on TV and say, ‘Oh Mommy. Oh Daddy.’ We try to explain that Mommy is going to work now. They always want to come to the set.

“Honestly, they think our work is in a trailer. That’s our office and their playroom on a set,” she says.

The gorgeous Watts who is the model of Ann Taylor and the star of previous movies including King Kong and Mother and Child lives with her significant other Liev Schreiber and is mom to two gorgeous young boys. She currently stars in Fair Game, coming to theaters November 5. It’s the true story of American spy Valerie Plame whose identity was leaked by the Bush administration. “I had just had a baby when I was sent the role. At first, I thought, ‘Impossible.’ Then I was told to read 12 pages and I was hooked.”

Read Picture of the Day: Naomi Watts

What do you have in common with the real Valerie Plame?
She’s very hard to get to know in a first meeting. I play it close to the vest, too. I like to read a person before I completely give myself away.

What was it like to meet the real Valerie Plame?
My co-star, Sean Penn, who plays my husband in the film spent time with Valerie and her husband in Santa Fe where they live now. I had just had a baby, so that wasn’t really possible. So I met Valerie for a few sessions before we started filming. Valerie and I were just careful at first and easy with each other. But then finally, it was crunch time and I just presented her with a list of very confronting and personal questions. I wanted to get into her mindset.

What amazed you the most about Valerie?
She was so unbelievably consistent and strong. I wondered how she could function when her identity was divulged.

You went through real CIA training. How tough was it while breastfeeding?
The first half an hour, they showed a video of people being killed in the most gruesome ways just so you would get used to it. The next thing I knew they had me handcuffed with my hands behind my back and thrown into a truck. My job was to get out alive.