Billy Idol's Guitarist Billy Morrison -- Wife Files for Divorce

Billy Idol's current touring guitarist Billy Morrison -- who has also played for bands like Camp Freddy and The Cult -- is finally going solo ... TMZ has learned, the rocker's wife has filed for divorce.

Morrison's wife -- Jennifer Morrison -- filed the docs just after the new year ... citing irreconcilable differences. The couple got married in 2002. They have no children.

According to the docs, the couple had been separated since September.

Jennifer wants the court to deny Billy spousal support. She also wants to restore her maiden name of Holliday.

Not to be confused with Jennifer Holliday, Tony Award-winning actress and star of the 1981 Broadway hit "Dreamgirls."