You can't file a joint return unless you are legally married. You would file separate returns. Most of the time, the person who pays more than half the family living expenses should file as head of household and claim the child as a dependent, and the other person should file single with no dependents. That usually results in the lower overall taxes. There are different combinations that are possible, if you wanted to know exactly what was best you would have to try them all on different test tax returns.
Just remember that only one of you can claim head of household, because it is impossible for both of you to pay "more than half" the household expenses. (If it is exactly half, no one can file as HOH, but the person who pays more than half only has to pay $1 more than half, if it is fairly close.)
And, only one parent can claim the child as a dependent.
