This will depend upon how many convictions he has. If he has more than two convictions, then he likely has a serious challenge, even if he is a lawful permanent resident. The DHS can only lawfully hold your husband for not more than 48 hours. Unfortunately, the jails are afraid to question the DHS or make the Feds do more work.
At times, there are other reasons why your husband can be held that are used as an excuse to hold him until the ICE Agency can make sense of your husbands criminal record and immigration status. Strangely, some lawful permanent residents may derive U.S. Citizenship without knowing it. Some of these U.S. Citizens have been deported by accident. Perhaps, some remain stuck outside the U.S. not realizing the situation.
I strongly recommend that you contact a candid and experienced immigration attorney like our office as soon as possible.
The above is general information not meant to be legal advice. This response does not create an attorney-client relationship.