It can take awhile until someone who knows how to advise you reads your question.
I'll give you my opinion until someone more qualified responds. I think that if the person who named your husband believes there is something going on, then there is no malice. So, I don't think your husband has any legal recourse.
Oh, believe me when I say there is malice. This man has spread this rumor over the town where he and his ex-wife live and even went to the people that my husband works for and told them. He has threatened my husband to have him fired. So, there is malice. He was using my husband to get his divorce on adultery so that he wouldn't have to pay alimony.
We are in SC and the divorce was not actually granted on adultery. My husband was never involved with this woman and he was never called to court. He was just named in the papers and the husband has been spreading these terrible lies all over the small town where this couple lives. My husband only works in this town.