You are in a difficult spot and have my sympathy. That said, you are not alone. Many people come here seeking advice about falling in love with another but want to keep their current relationship. And it's not uncommon that a woman falls for another woman but wants to stay involved with a husband or boyfriend.
Check out the poly relationship corner - lots of threads similar to your own. Search tags/keywords like jealousy and mono/poly. Other folks may suggest further ideas to search.
I do want to mention one more point. Jealousy is often how one's insecurities about one's self are expressed. Having a strong relationship, IMHO, requires a willingness to face and manage insecurity - I think this is true for all relationships but is critical for ethical non-monogamy. Nothing will push one's buttons like a partner's potential partners. You've experienced this when you acknowledge you feel very uncomfortable about your boyfriend seeing another woman. This is a really normal reaction. And it sounds like your boyfriend is experiencing similar insecurity and jealousy.
It is possible to work toward a mono/poly relationship where you see others and where your boyfriend is monogamous to you, assuming that would be his preference. But both of you have to be willing to deal with painful feelings and much uncertainty.