What should I do if my H1B expired and we're thinking of getting married?

In general, if a foreign national entered the U.S. lawfully and with inspection, and then becomes married to a U.S. citizen, the foreign national may apply to "adjust status" in the U.S. to become a Lawful Permanent Resident (to get a "Green Card"), even if the foreign national has overstayed his initial visa and even if he has worked without authorization. The process is known as a marriage-based adjustment of status application in the Immediate Relative visa category. It would be wise for you and your girlfriend to consult with an immigration attorney to review all of the relevant details about eligibility and to become represented in the application process. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.

You should have no trouble getting married. If she files for you, you should also get permanent residence. The only thing: talk to a lawyer prior to that and explain what happened with your work situation.