I wouldn't be ok with either. I am a massive overthinker, and always question why my husband is using his phone a lot, and why he only goes on Facebook when I'm not in the room, and what else does he look at. Would you feel the same way if he was messaging a male friend? I know i wouldn't. Have you spoken to him about it?
I think it’s weird if they frequently talk and he’s not spoken about her before. I still speak to a few male colleagues I used to work with but I’d class them as more of a friend than a colleague now. My husband has been aware of them since I had that job so he knows about their partners, their kids etc. and will ask how they’re doing. I know about female ex colleagues my husband still talks to and that doesn’t bother me as I’ve known he’s been friendly with them since they worked together. It would bother me though if he’d kept them a secret and spoke to them often. If he spoke to them a few times a year to say happy birthday and things, I don’t feel like I need to know about that but if they are talking every month or more often than that, I would be upset and suspicious that he’d not talked about her before and seemed like he was hiding it
I wouldn’t be ok with that! Why don’t you confront him and tell him it’s making you feel uncomfortable! X