If I am filing for my spouse’s green card should I file our income taxes as Head of Household or Married filing Jointly?
You can’t file as Head of Household if your husband is living in the U.S. The appropriate category for your green card should be Married Filing Jointly. The Head of Household applies if your husband is living outside the U.S. for a long enough period of time to qualify as a non-resident. IRS doesn’t use the term non-resident to refer to your immigration status, but where you live. There are tax consequences between filing as Head of Household vs. Married Filed Jointly. Circumstances vary and you should confirm with a Certified Public Accountant before filing, but generally you will pay more under Married Filing Jointly then Head of Household.
You don’t want to send to immigration anything that will undermine your case. An incorrect income tax returns, even if innocent, can still be considered fraud. You absolutely don’t want to submit fraudulent tax returns to immigration. It will undermine your case. You should filed amended tax returns before including them in your petition.