Despite there being rumors that Nicole Kidman and Keith Urban are headed for divorce, a source exclusively tells Life & Style the couple – who have been married for 11 years — are still going strong. “Nicole and Keith sometimes lead separate lives, with him being on the road and her on set,” the insider shares. “But they’re determined to make their marriage work. Despite going through ups and downs, they’re the best of friends and love each other very much.” A rep for Nicole tells Life & Style, the couple is “very happily married,” and says any reports of trouble are simply false.

Like many celebrity couples, Nicole and Keith, both 50, have to spend a lot of time apart because of work. Keith is currently playing festivals and promoting the April 27 release of his new album; he’ll kick off his 60-date Graffiti U Tour in June. Nicole spent February and March filming The Goldfinch in NYC, then headed to Monterey, CA, to shoot Season 2 of Big Little Lies in April. But the romance is still alive and well. “For every single night he’s away,” Nicole says, “he leaves me a love letter. Every single night of our relationship.”

The duo have gone to couples therapy, even spending five days at Marriage Quest, a private counseling retreat in Cabot, VT, earlier this year. “It was Keith’s idea to visit the boot camp,” says an insider. “They addressed a range of issues and learned to break down walls.” The parents of daughters Sunday, 9, and Faith, 7, both believe in the power of therapy. “They’ve overcome their marital problems in the past,” the source says, “and know they can do it again.”

The couple have been open about the problems they faced early in their marriage. Four months after their 2006 wedding, Keith — an admitted former drug addict who had gotten sober following a 1998 rehab stay — relapsed. “I’d go to sleep, wake up a couple of hours later, go at it again, drinking to take the edge off,” Keith recalled. “I remember thinking, I’m probably not going to make it until tomorrow.”

His addiction, he admits, “caused the implosion of my fresh marriage. It survived, but it’s a miracle it did.” That’s largely because Nicole fought so hard for it. “I was very, very blessed to have Nic call an intervention on me,” Keith says. He finally checked himself into the Betty Ford Center in Rancho Mirage, CA, and has been sober since. “For the first time in my life,” he recalls, “I could shake off the shackles of addiction.” It was a brutal time for Nicole. “It was painful, deeply painful,” she confessed in 2007. “We were in a very, very, very bad, painful place, and have managed to step through it.”

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Nicole and Keith have already survived intense struggles and come out on the other side. “Nicole stood by Keith during his recovery and feels that if they managed to get through that, they can get through anything,” the source says. He’s also been there during her toughest times. She was “shattered” by the loss of her father from a heart attack in 2014, she says. Keith was about to go onstage for a concert when she called to tell him the news. “He walked offstage and got on a plane,” she says. “He literally picked me up and pretty much carried me through the next two weeks.”

The secret to her happy marriage to Keith is simple: “Just love,” Nicole said in 2016. “Just love each other, lavish each other with love.” Also, she added with a smile, “We just happen to like each other, too. That works.”

For more on this exclusive story, pick up the new issue of Life & Style magazine, on newsstands now!