More information is needed. How many times has he been convicted? When was he convicted? What were the reasons for the conviction or convictions?
In many of these situations, but not all, a good faith marriage to a U.S. Citizen will not prevent a deportation.
You may want to find a way to hire an attorney to determine whether he will ever be able to lawfully return to the U.S., again. Also, which are the consequences for the crime of unlawful re-entry. You may want to locate a legal aid center that has attorneys who practice immigration law, where you qualify for such assistance.
The above is general information and does not create an attorney client relationship.