I think that decision would entirely depend on the nature of the crime(s) he previously committed before I met him, as well as the circumstances under which he committed the crime. If he stole food items from a grocery store in order to survive or to feed his family, of course that would be somewhat understandable. If he by accident became associated with the crimes of one of his friends (he was at the wrong place at the wrong time) I would also understand. I think where I would draw the line, however, would be violent behaviors that got him in trouble with the law, such as armed robbery, rape, physical abuse of any type, or drug trafficking. These types of behaviors would strongly cause me to question his ability to have reformed himself entirely. A person with a violent past typically does never change 100 percent, and I would never be truly able to find myself at peace with him around me, not knowing what specifically may trigger an outburst of violent behavior.
I would also wonder why he did not previously mention his past to me or how I could have missed out on so much about this person prior to marrying him. Was he hiding these incidences from me? Was he doing such a good job at it that I was truly not able to find out anything negative about him until now? If so, was he only putting on a front until he had me locked in? Also, did he feel that he could not completely trust me with this information, even though we are supposed to spend our lives together? I would consider the source of this information. Did he tell me about his past himself (if so, why all of a sudden now and not earlier? What triggered his confession to a criminal past) or did I find out through a third person? If it was another person, who was it? A friend, a family member, a former accomplice, etc.? Did this person maybe have a reason to try to get back at my husband and blurt out the story of his past to upset our marriage? All these are factors needing consideration before I could think about how to respond to this new and undesirable information.

Past is past, but I think he should come clean and let you know everything about him.