The couple were married July 29 on a yacht in St. Tropez. Then they tied the knot twice in August in a civil ceremony in Beverly Hills and at a honky tonk in Nashville.
Rock, whose real name is Robert Ritchie, filed a separate divorce petition, within an hour of Anderson's, early Monday. Anderson reported their separation date as Nov. 21; Ritchie said it was Nov. 26.
Both cited irreconcilable differences as the reason.
On her Web site Monday, Anderson posted a message that said, "Divorce Yes, it's true. Unfortunately impossible." A picture of the pair appeared next to the statement.
Earlier this month, US Weekly magazine reported that Anderson confirmed that she suffered a miscarriage. Anderson's rep asked that "Pamela's privacy be respected at this time."
Anderson and her first husband, rock star Tommy Lee, divorced in 1998 after three years of marriage. They have two sons, Brandon, 10, and Dylan, 8.
Ritchie, has a 13-year-old son, Bob Jr.