I'm sorry he lied and led you into this. He should have been upfront about his intentions with you once you guys become serious. It sounds from your post that you're not interested in sharing his love, and that's OK, and you were honest with him about it. If he says his other relationships are "non-negotiable" you have a choice to make. Stay with him and try to learn about this lifestyle and try to make peace with it, or move along and let him go. The fact that he was dishonest does not bode well for you guys in any event. There are MANY honest, honorable people with open marriages out there, but you got involved with one who is not.
I know 4 months can seem like a long time, but in the overall scheme of things it's not really. I think you'll be doing your emotional health a great disservice to try to put up with him and his lies.
Keep posting and let us know how you're doing. And try to divide your posts up into paragraphs to make them easier to read. Some people will see a VERY LONG paragraph and not even want to read it.