My husband sent a message to a woman, calling her dear, baby, saying that he couldn't sleep at night and wanted to know if she meant having an affair. What should I do?

Maybe just for fun, looking for ambiguity and excitement. As long as you are clear-headed, you will not be emotional, but you will definitely hurt your wife's feelings. I suggest you calm down first. Don't point it out, but let him know what he is doing, right or wrong, and let go in time. Let him know that you are independent, not that anyone can't live without you.