My boyfriend hooked up with my friend while we were broken up...?

So my boyfriend and I were together for a year and half. I'm only 19 and I know that I shouldn't waste my time on a boy, especially one with whom I've had such a rocky relationship. I broke up with him earlier this year because at the time he was clinging to me and more or less suffocating me, but I regretted it the very next day. We were only broken up for about four days, but in that time he hooked up with a close friend. We were back together for a couple weeks and I could sense something in the dynamic between the two of them, but when I asked about it he told me he didn't like her like that and so on. Well we've been broken up for about a week and a half now, this time his doing, and last night he just informed me that he had lied about there being nothing going on between them. Neither of them told me about it. This isn't exactly the first time something along these lines has happened with him, and I know the rule about infidelity and dishonesty, that once it happens you should kick him to the curb. We were talking for a long time last night and he wants to try to just be friends and see what happens. I don't really know what to do. Should I cut him out of my life entirely, or should I try the friendship thing and see if he can make this up to me by being a good friend? Oh and what the hell should I say to her? She hasn't spoken to me much in a month or so, and I haven't seen her in longer but any time we talk she acts like everything is hunky dory. I know better than to cuss her out and call her rude names because it doesn't sink in, but I can't let it go that she thinks I don't know. What should I say to her?