If you want to keep your marriage, and keep it a happy one, lose the male riding partner. I'll probably get flamed, but this is an important issue to me. My husband and I make a point not to spend one on one time with people of the opposite sex, especially on an on going basis. We hang out with people of both sexes in a group setting.
This is not necessarily a trust issue or even an "ego" issue. Just a smart way to keep a healthy marriage.
By doing this, we eliminate any issues of possible jealousy, gossip from other people who might not know how platonic the relationship truly is and, of course, any possibility of infidelity. Most every extra-marital affair starts out as "just friends". Few spouses actually "plan" on sleeping with their "buddy" of the opposite sex, but the more time you spend with someone, the more opportunity you have of a spark getting ignited.
And above all else, the fact that your husband is not happy with this situation should be reason enough to avoid it. He should be number one in your life. His feelings and concerns should be more important than spending time with another man. He SHOULD be jealous of you spending time with another man.
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So there's my two cents worth.
