Playing Kim Basinger Refers to Her Marriage to Ex Alec Baldwin as 'Sleeping With the Enemy'. Kim Basinger says she's cool now with her ex-husband, Alec Baldwin, but that wasn't always the case. Basinger and Baldwin were married from 1993 to 2002, and in an interview with Net-A-Porter's The Edit, the 62-year-old actress sort of jokes about just how bad her relationship with the 58-year-old actor became. There were times I could have chosen [my movies] better.