Sheen, 45, seeks joint physical and legal custody of their 1 1/2-year-old twin boys, while Mueller wants primary physical custody with visitation for Sheen, according to the papers filed in Los Angeles Superior Court.
Both cite irreconcilable differences as the reason for the split and agree they separated on Christmas Day when they had a nasty fight in Aspen that landed Sheen in jail.
Sheen and Mueller have both since entered rehab in separate programs. Sheen was also placed on probation and sentenced to domestic violence counseling.
Sheen recently was hospitalized for a day in New York after he was found reportedly naked and disoriented in a hotel room. Police sources say he was drunk; his rep says he had an allergic reaction to medication.
At the time, Mueller spoke out in his defense, saying, "You know how things get blown out of proportion."