I had another thought on this. If envy or jealousy arises in a romantic partnership, generally I'll work on that very hard with the partner. I'll also work on it with the respect for the love and care we've built together. I think most people would approach it in a similar way.
I hold my friendships in life to be just as important as my romantic partnerships. So why would I treat a jealousy or envy issue with my friend any differently than I would treat it with my partner?