David M. Rubenstein and his wife, Alice Rogoff, at the 2016 Kennedy Center Honors in December. (Jahi Chikwendiu/The Washington Post)

A court filing this week offered a rare peek inside the marriage of top-dog philanthropist David Rubenstein, who made his billions as the co-founder of the private-equity firm the Carlyle Group, and his wife, former Alaska newspaper publisher Alice Rogoff.

A statement from Rogoff, submitted in bankruptcy proceedings for the media company she owned, immediately set tongues wagging in Anchorage, where the rise and fall of her business — as well as her ultra long-distance relationship with Washington-based Rubenstein — have been closely watched. In the document, Rogoff referred to a “marital settlement agreement” with her husband of 34 years.

That kind of agreement is usually a precursor to divorce — in which a married couple spells out how they’re going to handle things like property division, child custody and spousal support. But a person familiar with the arrangement says in this case, no divorce is currently in the works and that the agreement provides for Rubenstein’s annual payments to his wife, a use of marital settlement agreements sometimes employed by married rich folks who want separate finances. It’s been in place for “many, many” years, the source says.

The couple, who raised three now-grown children at their home in Bethesda, have an unusual arrangement — she spends most of her time in Alaska, while Rubenstein, 68, has remained in the Washington area, where he is the chairman of the Kennedy Center’s board of trustees and a major donor to an array of causes. Last year, he donated $18.5 million for the restoration of the Lincoln Memorial, and he recently pledged millions to cover the tab for updating the elevators of the Washington Monument and gave $20 million to Monticello for projects highlighting the history of slaves at Thomas Jefferson’s estate.

Rogoff’s own description of their relationship is cryptic. Asked about it at a meeting with reporters and editors of the Anchorage Daily News after she bought the paper in 2014, she reportedly said only that “it’s complicated.”

Still, the couple were seen publicly together at glitzy events, including at the Kennedy Center Honors gala in December and at then-President Barack Obama’s state dinner honoring Chinese President Xi Jinping in 2015.

The financial agreement between the two also answers some questions about the finances of her bankrupt Alaska Dispatch News, which reportedly owes more than $2 million amid a slew of legal and financial woes.

“The struggle to make ends meet financially eventually caught up with us,” Rogoff, 65, wrote this week in a message to readers following news of the media company’s bankruptcy and new owners. “I simply ran out of my ability to subsidize this great news product.”

According to her statement in the bankruptcy case, Rogoff used the payments from the agreement to help settle a $13 million loan she took out in 2014 to purchase the Anchorage Daily News, which she folded into the media company she started in 2009.

Rogoff did not respond to voice mails seeking comment, and a representative for Rubenstein declined to comment.