By Jodi Guglielmi
Updated September 26, 2016 at 11:24 PM EDT
Credit: Taylor Hill/FilmMagic

Naomi Watts and Liev Schreiber have split after 11 years together, PEOPLE confirms.

“Over the past few months we’ve come to the conclusion that the best way forward for us as a family is to separate as a couple,” Schreiber and Watts said in a joint statement to PEOPLE.

“It is with great love, respect, and friendship in our hearts that we look forward to raising our children together and exploring this new phase of our relationship. While we appreciate your curiosity and support, we ask the press to be mindful of our children and respect their right to privacy,” the statement continued.

The two are parents to Alexander (Sasha) Pete Schreiber, 8, and Samuel Kai Schreiber, 7.

Watts, 47, and Schreiber, 48, met at the Metropolitan Museum of Art’s annual costume ball in 2005 and immediately hit it off.

“We spoke on the phone for several weeks and emailed,” said Watts, who had to return to Los Angeles at the time. “And then I made up some excuse to come to New York and the rest is history.”

The couple often enjoyed family time together at their home in New York City where they were frequently spotted spending afternoons in Central Park and running errands with their brood.

Watts and Schreiber even traveled to Australia together to spend the holidays with her family.

But their relationship was the subject of scrutiny over the years, particularly over the issue of marriage.

In 2012, Watts told Easy Living Magazine that marriage simply wasn’t a top priority for the couple. “We’re very much together. We just don’t have that certificate, and that’s okay with both of us,” she shared. “Maybe one day, we’ll just wake up and go ‘Hey, let’s do this.’ And maybe not.”

Watts and Schreiber have appeared in several movies together over the years, including The Painted Veil in 2006 and Movie 43 in 2013.