According to the IRS:
If you are a resident alien, the rules for filing income, estate, and gift tax returns and paying estimated tax are generally the same whether you are in the United States or abroad. Your worldwide income is subject to U.S. income tax the same way as a U.S. citizen. You are a resident alien of the United States for tax purposes if you meet either the green card test or the substantial presence test for the calendar year.
As far as whether you should file jointly or separate, I can't say for sure, but it is almost always more advantageous to file jointly. The only way to know for sure would be to calculate it both ways.
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