I do believe you can have platonic long-term friendships with the opposite sex. I have a friend who is a guy who I've known for a decade and I've never been attracted to him and he's never shown attraction to me, but we like to hang out together and get coffee. I had another friend like that, we're not really friends now because we've grown apart, but we were for a long time and there was never anything sexual about it. I would be upset though if I found that my significant other was making derogatory comments about me to someone else, male or female. I can understand how that would upset you.