I don't think you're mad at all.
I'm very accepting of opposite sex friendships - my husband goes out to lunch with female friends often, and I have male friends who I do the same with. I've never once had a worry about any of them.
With an ex of mine, it was the same, right up to the time he met 'H'. She was recently divorced and they became good friends. Not a problem... that was until I noticed that she started doing things like texting him a 00.01 on his birthday to say Happy Birthday, and late evening texts, early morning texts etc.
He was happy to show them to me - without my asking. I warned him that she was after him, and he swore they were just friends and she was just trying to get a social life together after her divorce. I was apparently jealous and imagining things.
Then she invited him to a party in the city where she lived - 2 hours from where I lived. Since it was so far, he could stay at hers, she had a spare room. I offered to pay for a hotel and he said I was mad, he didn't fancy her and didn't I trust him. I said I trusted him fine, but what did he plan to do when she climbed into bed with him naked?
I have no idea what actually happened, but the night of the party, ex turned up at mine at 4am - there was never another text or phone call or anything from H again.
It's the only time I have ever felt anxious and I suppose jealous, and it appears I wasn't reading things wrong.
There may well be nothing in it from one or other side. I'm pretty sure my ex just 'didn't get' what H was thinking and up to - despite my spelling it out. I don't think it's 100% harmless platonic friendship. Your husband is behaving a bit lovesick. Question is what to do.
I think the dinner may well be a good idea. I hope it goes well. Just don't feel that you are going mad and imagining things. I don't think you are in the sense that there is an abnormal level of interest, but I don't think it means that there is an affair or anything of that sort going on. But it is a potentially dangerous situation for one or other or both making complete fools of themselves.