If my husband didn't have any income to claim, am I head of houseold? Am I filing jointly or separately. We should qualify for the earned income credit, but I'm not sure how to file. I think I'm head of household

You are not head of household.
You can file as married filing jointly (MFJ) or married filing separately. In most cases, it is better to file as MFJ. If you file MFS, you will not get many credits and deductions.Read Your U.S. Tax Return: Filing Status for Married