If you are considered a Resident Alien for tax purposes, then your choices for filing are Married Filing Jointly or Married Filing Separately. You have the choice as to which way you file.
If you have children or are in college, then it is generally better to file a joint return so you can claim all the credits. When you file separate returns, you are not eligible to claim education credits, child and dependent care credits or the Earned Income Credit.
You can also use the Tax Calculator for an estimate on if you will make out better filing a joint or separate returns.