"I cannot participate in anything critical about my children's father," the My Super Ex-Girlfriend star says in the upcoming issue of Parade magazine. "I just need to keep peace. I think it's fair to say that I haven't said one mean thing, and I'm not going to start now. It's terrible for my family."
Thurman, 36, and Hawke, 35, met on the set of the sci-fi drama Gattaca and married a year later, in 1998. They had two children, daughter Maya, now 8, and son Levon, 4, before Thurman filed for divorce in 2004 amid rumors that Hawke had been unfaithful.
Of the split, Thurman – who refers to Hawke only as her kids' dad – says, "If I see one more headline about it, I'll gag. I'm just another American woman who was in an unfulfilled marriage that fell apart."
But the actress, who was married to actor Gary Oldman from 1990-92 and has been in an off-again, on-again relationship with hotelier André Balasz for the past two years, admits she's sometimes baffled by relationships.
She adds with a laugh, "I'm working on a decoding system – especially for men."
Still, persistence itself has been an achievement. "One thing I'm proud of, which is not an easy sentence for me: I'm proud that I keep trying," she says.
"It's been very helpful for me to discover that I could do that. Sure, there are challenges. Sure, there were dark things. But I have a great career and two healthy, beautiful, smart and funny children. We're an incredibly tight-knit threesome, and we have so much fun together."