In general, if you are a U.S. citizen or resident alien married to a nonresident alien, you are considered “Married Filing Separately” unless you qualify for a different filing status. If you pay more than half the cost of keeping up a home for yourself and a qualifying child or other relative, you may qualify for the head of household filing status.
If you are a U.S. citizen or resident alien married to a nonresident alien, you and your spouse can choose to have your spouse treated as a U.S. resident for all U.S. federal income tax purposes by making the §6013(g) election. This allows you and your spouse to file a joint return, but also subjects your nonresident alien spouse’s worldwide income to U.S. income tax. IRS Pub. 519, page 9, has information on how to make the election.
If you file a joint return, you can claim an exemption for your nonresident alien spouse. If you do not file a joint return, you can claim an exemption for your nonresident alien spouse only if your spouse has no income from sources within the United States and is not the dependent of another U.S. taxpayer.