'Homeland' Star -- Husband Demands Cash & Custody In Divorce

"Homeland" star Morena Baccarin's growing success could be exactly what hurts her in her divorce ... costing both money and time with her kid.

Morena's soon-to-be ex-husband Austin Chick just filed docs in their divorce, and he wants his chunk of her paycheck. Chick claims Morena is pulling in $1.5 million a year. He wants a cut for child and spousal support.

Chick says Morena's constant travel for work isn't healthy for their one-year-old, so he wants physical custody. He also wants Morena to cover nanny expenses up to $3k per month.