09/25/2009 AT 03:50 PM EDT
Although his relationship with LeAnn Rimes played out under a media glare, Eddie Cibrian's divorce from his wife Brandi Glanville promises to be less explosive. "Both sides are hoping to settle their divorce amicably," a Glanville source tells PEOPLE.
Los Angeles Superior Court records show that Glanville, citing irreconcilable differences, is seeking spousal support from the CSI: Miami
star as well as physical custody of their sons Mason, 6, and Jake, 2, with visitation for Cibrian. The actor filed for divorce
last month and is also seeking shared custody.
Earlier this month, Rimes announced on her Web site
that she and husband Dean Sheremet were divorcing following months of rumors of her affair with Cibrian.
Cibrian, 36, and Rimes, 27, met while filming the Lifetime movie Northern Lights last fall.