Elizabeth Vargas, Marc Cohn divorcing, report says

"20/20" anchor Elizabeth Vargas, who said over the weekend she was entering rehab to deal with long-standing alcoholism, reportedly is now also facing divorce.

People magazine said Wednesday that Vargas, 51, and her husband, singer-songwriter Marc Cohn, are in divorce proceedings, adding that their sons, 11-year-old Zachary and 8-year-old Samuel, are in New York with Cohn while Vargas seeks treatment. The couple married in 2002.

"On behalf of Elizabeth's family," Cohn told Newsday in a statement, "we are in total support of her recovery and want her to be well." He did not address reports of divorce, and neither his representative nor ABC News had an official comment.

Cohn, 55, the 1991 Grammy Award-winner for Best New Artist, is currently on break from touring, the magazine said. His website retains tour dates beginning in October. He is also listed among the performers in a concert tribute to Billy Preston at City Winery in Manhattan on Tuesday.

Vargas went public with her alcoholism in November, saying in a statement then, "Like so many people, I am dealing with addiction. I realized I was becoming increasingly dependent on alcohol" and that she was "in treatment."

In a January interview with "Good Morning America" co-anchor George Stephanopoulos, she said Cohn had recognized the alcoholism for which she was in denial. " 'You have a problem. You're an alcoholic,' " she recalled him telling her. His declaration "made me really angry, really angry," she said. "But he was right."