DH and I have been together for 20 years and have DC aged 12 and 14. We have grown apart a bit since having the DC and haven't had sex for several months, but we still get on fine.
He has become very friendly with DD's cello teacher over the past couple of years. They text one another a lot, and email; he also seems to find all kinds of opportunities to speak to her (apparently about DD). I've looked at his phone and computer (I know I shouldn't, but I'm too worried not to), and there's nothing at all sexual about any of their messages, though they mostly end with kisses. They seem to send one another stuff like funny headlines and jokes, and there's nothing romantic there - but I hate it all the same.
I did tell DH that I'm not happy about it, and that he wouldn't like it if I had that kind of friendship with another man - but he said I was making mountains out of molehills, and that they're just friends. He also says that if anything had been going to happen, it would have happened by now. I think it's disrespectful to me to continue this friendship even if there's nothing affair-ish about it, because it makes me unhappy - but he thinks it's disrespectful to him to suggest that there's anything in it other than friendship.
What do you think? AIBU to object to it?