I don't know if this is cheating, but he'd better stop this kind of thing at once. Texting often proves that at least your husband doesn't dislike her texting, and even has a good impression on this person. If a person hates someone, he will never chat with them. She belongs to a karaoke bar, so there will always be something worthy of men's liking, such as her appearance, singing skills or understanding. It hasn't developed yet, but no one knows when something will happen to such a woman who is soft and hard around him. Maybe you'll be the one who gets hurt. Just make it clear to him that you don't like his association with that woman, and then if he loves you, it's okay to lose a friend of the opposite sex. Men and women are right and wrong.