'Homeland' Star Morena Baccarin -- Real Marriage Blows Up Too and It Could Cost Her $$$

Morena Baccarin -- Nicholas Brody's estranged wife on "Homeland" -- is headed for divorce off-screen too -- and all her success since the Showtime hit could work against her in the split.

Baccarin’s writer/director husband, Austin Chick, filed the divorce docs, citing irreconcilable differences, after 3 and a half years of marriage -- a lifetime in Hollywood.

According to the docs, Chick wants joint custody of their one-year-old son ... and he wants spousal support.

It looks like Baccarin's been the breadwinner in the fam -- picking up roles on hits like "Gotham" and "The Flash" -- so, at least on paper, she'll likely end up forking over some amount of cash.

Did we mention she's banging Det. Jim Gordon on "Gotham?" 'Cause she is ... and she looks freakin' hot doing it.