You can also elect to file jointly with him (rather than filing separately) if you want to. Once you make this election, you must continue to file jointly with him. At some point, you may change your minds and cancel the election. After you have cancelled the election, you can not re-elect to file jointly for at least five years.
Alternatively, you file a 1040 as either (if you have kids) Head of Household or (if you don't) Married Filing Separate; and you husband files a 1040NR (if he has any US source income) as Married Filing Separate.
You would only file jointly with him if he doesn't make much money. If he makes more money than you, or about the same, you'll probably save much more money filing apart.