It appears you need to try for one anyway. His tax status is definitely a problem though. He should correct the last three years if possible ASAP.
If your employment is not authorized, then your income does not count for the affidavit of support. Your husband must file an affidavit of support even if he gets a joint sponsor, since he is the petitioner.
You will need a separate joint sponsor. Your employment can be used only if you have valid work authorization at the time of filing. If you can get the joint sponsor and file as soon as possible you should have work authorization within 90 days of filing your petition.
An Affidavit of Support is always needed for the adjustment of status (green card) application. You can get a cosponsor. You can also obtain a work permit based on the pending green card application.
An attorney-client relationship is not formed by my responses to questions on Avvo. My responses are not intended to be legal advice and must not be relied upon as legal advice.
If your husband sponsors you and you can apply at the same time for a green card (only if he is a citizen), then he will have to complete the affidavit of support but you will need a co-sponsor. If you can file for a work permit at the same time that you apply for residency as the spouse of a U.S. citizen.
You should consult with a competent attorney or BIA accredited representative to assess any possible fraud issues in your case (in the event that you had met your husband before you entered the U.S. or before you applied for your f-1) and any other inadmissibility issues that may arise.
Daniel Green, Esq.
Serving the Hudson Valley, Northeast U.S. and the World
Location: 684 Aaron Court, Kingston, NY
Mailing Address: PO Box 3238, Kingston, NY 12402