I'm not sure which is harder to deal with -- emotional relationships or physical relationships. I suppose it is different for different people.
Please understand that I am shooting from the hip here, but it seems to me that emotional relationships are likely very common. Blending the "I really like this guy/girl" with "I want to have sexual relations with him or her is wherein the situation becomes out of control for married or otherwise attached people.
While in undergrad school, I had what I thought to be a purely platonic relationship with a fellow student who was ten years my senior. She was married and had children, yet she willingly went to a bar with me to discuss poetry. [It was the class we had in common].
Driving back from a night of drinking, she told me that she and her husband had come to an understanding about having sex with other people while remaining committed to their marriage. Still regarding her as a platonic partner, it didn't even sink in with me that she was throwing out an offer to have sex with. That I realized the next day while thinking about her statement. Although I liked her and found her attractive, I began to separate myself from her company, and nothing physical ever happened between us. After all, she was a married woman.
I don't think platonic relationships are a violation of ones marriage vows. It is when lust arrives that the relationship begins to go too far for a married person.
That your husband confessed to you his feelings for her corroborates his belief that it is innocent at this point. It also seems to indicate that he has an inkling that maybe it isn't innocent after all. Why else would he even bring it up.
You are entitled to be jealous of his relationship simply because his feelings for her have progressed beyond the platonic. If your marriage is strong, one of the two of you will have to make a change. He will have to stop his relationship with her to prove that he is loyal to you and doesn't want to be the cause of you feeling depressed [and probably angry and afraid]. That, or you will have to accept that men often become physically attracted to female friends even though they have no intention of taking it any farther. Of the two options, I believe him taking action to severe ties with her is the easiest to accomplish. Jealousy and insecurity are deep seated emotions that can be pushed under but never fully eradicated.
Dave, two daughters: Echo and Holly. Hence the screen name -- DavEcHolly