“We go forward with love and friendship for one another and a commitment to co-parenting our children whose privacy we ask to be respected during this difficult time.”

They said this will be their only comment “on this private, family matter. Thank you for understanding.”

The couple have three children, two daughters, Violet, 9, and Seraphina, 6, and one son, Sam, 3. Their 10th wedding anniversary was Monday.

“Ben and Jen,” or “BenJen” in tabloid parlance, first went public as a couple when he took her to the opening game of his beloved Boston Red Sox World Series games in October 2004.Six months later he proposed, on her 33rd birthday.

Garner, 43, married Affleck, 42, her second husband, on June 29, 2005, in a private ceremony at a resort on the Turks and Caicos Islands. The officiant was Victor Garber, her co-star in the popular series that made her a global star, Alias.

Since then, his career seemed to soar while hers seemed to subside, as she focused on raising their children. She has had a steady series of smaller or supporting roles, in films such as Juno, Dallas Buyers Club, Butter and Alexander and the Terrible, Horrible, No Good, Very Bad Day.

According to the Internet Movie Database, she has at least two movies scheduled to come out in 2016.

Affleck, who’s playing Batman in the forthcoming Batman V Superman: Dawn of Justice, has just come off a big hit with Gone Girl, not to mention Argo, which he also directed and which won for best picture.

They were an attractive and appealing couple, active politically, public-spirited, and frequently profiled in magazines as a seemingly perfect celebrity couple. But all was not well in paradise.

Last month, US Weekly magazine published a cover story quoting unnamed sources as saying the couple were “fighting for their marriage.”

Rumors of marital woes have dogged them for years. When Affleck picked up a second Oscar, for Argo in 2013, some thought it significant when he referred to their relationship as “work” in his speech.