Your situation is not an uncommon one. You basically have three options.
1) Decide to leave. Maybe this really isn't for you. That's ok! It's perfectly fine to need to be your partner's one and only. I know you said you couldn't ever bring yourself to leave, but is that really healthy? Love may be real, but that doesn't mean the situation is right, and you *will* love again. Maybe you need to be strong and pick up and move on. It's not a judgment against him, just a recognition of your needs and limits.
2) Decide to try to reconcile with the idea of non-monogamy. You could ask him to wait while you work on this. Set a time period, like a month. That will give you a chance to, among other things, feel sure that you can trust him. But you have to hold up your end of the bargain and really do your homework. Check out books like The Ethical Slut and websites like www.morethantwo.com
, especially the resources on jealousy. Work on really believing that he's not trying to replace you, that you are, in fact, irreplaceable because no one else could ever be *you*. Even if he loved someone else exactly as much as he loved you, you would still be you, and you will always be special.
Try to understand, ask him to explain -- does he really want relationships with others, is it just sexual non-monogamy that he wants, or does he actually want to, at least potentially, love other people? Understanding his motivations and what you can expect will at least make it less confusing, if not less scary. Know that it's ok for you to ask for things you need, even in this context. For instance, do you need there to be guidelines about safer sex, about checking in, do you need to meet someone he wants to sleep with before he sleeps with them? All of that is ok. You guys can work out whatever system works best for you.
Then, when the allotted amount of time has passed, suck it up and let him go out and be with someone else. Spend the night with a friend, drink if you have to, cry. Give yourself a chance to see how you feel the next day, and in a few days after that... even worse, or beginning to be ok? If the former, revert to option one. If the latter, maybe you're more adaptable than you think, and you guys can have a healthy mono/poly relationship.
3) Decide not to decide. Let him sleep with other people, but don't attempt to reconcile yourself to it, and just be angry and miserable. Obviously I'm saying this one as a bit of a joke but, unfortunately, this is the path some people take. Don't let this be you.