I know you said you wouldn't want to be very specific OP, but the description is very surface level, it is hard to guess if there is anything to be worried about.
Speaking as a man who has female friends - one of my best friends I have known since I was 13, that is a 25-years old friendship. I have known her longer than my wife. We are very close, talk about a lot of things, relationships, mental health, family drama, you name it. And yet, my wife has nothing to worry about - and she knows it, not even a little bit of a worry there. We were at her wedding last year, she was at ours.. If my wife ever had a problem with our friendship, I would then of course resolve the matter, i wouldn't let my own spouse feel bad, sad, worried or anything..
Just wanted to say, that friendships like that exist - and I don't know your DH, don't know their friendship, not saying there is anything to worry about or isn't...as there are no details. Just wanted to share my thoughts and experience.
One thing though, if you don't trust him, or you have an issue, staying just to "let her win" is not a great mindset to have, sounds very uncomfortable... Does DH know it at all how you feel? I am just guessing here that he doesn't, based on the last bit of your post.