Help? Need cheating advice!

Soooo I've never done this so bear with my here k? Ok here we go.
My girlfriend has cheated on me...twice now. And before you ask how I know, she told me. Right after each time. The first time she was crying, calling herself a terrible person, saying how sorry she was, saying she'd never do it again (even though she said she'd never do it in the first place) hoping I could forgive her blah blah blah. I always thought that heart broken was an expresion ya know? Except after that it felt like my heart was litterally broken. I couldn't stop throwing up...it was bad. I won't get into it much but long story short (too late?) after a couple days of her crying and me drinking/smoking way too much we got back together and started working it out. I know I know once a cheater always a cheater. Buuuut I really care for her. She makes me happy. I love her and I didnt feel like throwing away 9 months just for one stupid gut wrenching heart tearing mistake. Oh, and he has a smaller you-know-what than me. So that makes me happy. Anyways, so recently (as in last night) she cheated on me again. This time when she told me she wasn't crying, no begging for forgiveness stuff. She kind of acted like it wasn't a big deal. Sure she apoligized and stuff, got all sad and did the whole I'm sorry don't leave me I love you thing...but her voice was like "whats the big deal?" And some people would say it isn't. See here is the twist. My girlfriend is bisexual. Last night she cheated on me with a girl. And now...I'm really confused. So here is my question for yall.
Is cheating with someone of the same sex when your in a relationship with someone of the opposite sex still cheating?
Cause see I'm on both sides. When she told me this girl was bi I teased her about lesbian sex that night and she got all mad at me. "I know that'd upset you, so I wouldn't do it". I replied I'm not sure how I'd feel...I'm still not. See cause I understand that your bi and you like both and after a long time with one you kind of want the other a little...with a guy I'd wonder what does he have that I don't. With a girl I know what she has that I don't. And also, the inner sexist says so what it's really hot.
But on the other hand.....she said she wouldn't. And thats whats really sticking on me. Thats what I cant just ignore. She said she wouldn't...and she did it anyway.

So loyal readers. If you have made it this far, I assume you have no life and could spare a few minutes to drop me a comment. Answer above said question, dig deeper into the story (that could also be done with messages), leave some friendly advice (again messages work), or just simply critique my writing style (see above parentheses). Thanks for reading! Hope I didn't bore you to death.
Now leave a freakin comment. Or shoot me a message. Your choice.