Your GC won't be affected. Your hu*****and's case may involve so called "Crimes of moral turpitude".If he is found "Inadmissibility" under this ground, GC is difficult for him. There is an exception, called "petty offense exception". The criteria are that the maximum penalty under the particular criminal law is no more than a year in jail and the sentence actually imposed was not more than six months in jail. In order to establish that one qualifies for the exception, your hu*****and must provide the actual state criminal statute clearly outlining the nature of the offense and the penalty at the time the offense was committed. It is also necessary to submit the court record, showing the charge and the sentence. If those documents are unclear, it may be necessary to provide a letter from a criminal law attorney to explain the document to the CIS officer.
The issue is very complicated, I suggest you contacting a lawyer for a detailed discussion and bring him/her to your hu*****and's interview.