Cochran, 39, cited irreconcilable differences as the reason for the split, claiming her 43-year-old husband is addicted to drugs and has a 22-year-old girlfriend, TMZ reported Monday.
Cochran is seven months pregnant with the couple's third child. They also have a 5-year-old son and 8-year-old daughter.
The former couple both appeared on TV's "Burn Notice."
2014: The Year in Music [PHOTOS]