Breaking agreements and trust is always hurtful. But, to me, the deeper question is ... Is there love between you? It is loving that you want between you, I presume (?).
The fact that he came clean and told you what happened should be encouraging. He could have never said a word.
I'd also recommend looking at what this kiss means to you, and why. Why does it hurt you so much that he kissed this other woman? --aside from the agreement-breaking, that is.
I'd say... open to this hurt, welcome it, let it have its own fullness of expression... and while you do this, explore any past hurts that come up in the process. Open to these, as well. Whatever you do, don't turn away from the emotional pain until you come out the other end of your process--whatever that may be. I think you'll be surprised at the freedom and love that will emerge if you become intimate with yourself in this way.