I appears that he should be able to adjust status under section 245i of the INA, since he is the beneficiary of a petition filed before April 30, 2001. All this assuming that you are a United States citizen and that he is otherwise eligible to become a permanent resident (For example, if he has committed a crime that might or might not affect his eligibility for adjustment of status).
It is not very complicated case if you are a USC or LPR. He is grandfathered. Talk to a lawyer. He is also eligible for DACA.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.
It sounds like your husband has a couple of options depending on your immigration status. He may be eligible for adjustment of status under 245(i) or DACA.
Please note that this response is for informational purposes only and does not create an attorney-client relationship.
You will have to resolve your husband's status sooner or later. You can file for him to obtain an Immigrant Visa (I-130). He is grandfathered in by his step father's I-130 filed in 1998 so if he entered the U.S. illegally he can pay a $1,000 penalty and adjust status here, if you are a U.S. citizen. If you are an LPR then you will have to wait for the priory date to become current. You should definitely seek an attorney's help with the petitions.
It looks like he should be able to adjust under 245i. Please consult with an immigration attorney.
This answer is of a general nature and should not be relied upon as final, nor is it intended as legal advice. Consult with a qualified attorney before making any legal decisions.