Well I see from reading more that he not only was deceiving you but himself also. It seems the two of you have some learning to do about how poly can work. I stand by everything I say, even if he was a shmuck for not facing his fear and fighting that well learned feature of our culture, lying.
You asked what you should do now? I suggest doing some searches here, start with a tag search for "cheating" and "jealousy" and "boundaries" Then look at the stickies and find the thread on lessons learned and poly foundations... you can do a tag search for those too.
I would suggest getting on a heavy, honest conversation about boundaries and see how to work this woman in your life. He fucked up by thinking he could just be friends, but it isn't the end of the world, just time to look towards the future knowing that. For both of you.
Looking towards the future as soon as you can would be best I think... the longer you spend drowning in sorrow on either side the worse off. I don't mean that you should do things rashly, but get on talking... the only thing I think needs to happen quickly, as soon as it comes up and as often as is necessary is communicating. You don't have to agree to have him see her right away, but a time line for that happening. What will happen then. What you plan to do to deal with it. What you expect from him. What you expect from her. What kind of process you hope to use to get through this. Remember to keep it as fluid as you can... that way if something doesn't work, it can be changed after re-negotiating. You have a lot of work to do and a lot of questions to ask... when you are able to rise above the emotions, get to work.
*hugs* I feel for you both, really I do. I know what this feels like all too well