I cannot say about his loyalty; I guess it is upto you now to trust or not.
But strictly from immigration point of view, when did he apply for green card? It could take years and years before he is approved if he is going through normal process of employment based Green card. Has he included you in the filing? Make sure he has; otherwise it will take forever for you to get a green card after he gets his.

This is a serious matter and you have to discuss this with your husband and gauge where this is going.