"Why" doesn't matter. What matters is that he did.
I always have a problem with people trying to figure out the why, what did I do, hwo he could he/she do this...and so on.
As far as the girl...I'd leave her out of it. Yep, she's a scum for cheating with a married man...not something I would do, but also not your problem. Why, you ask? Because no matter how willing she was to cheat, if your husband didn't participate, there would be no issue. So blame the right person.
As far as what to do...you've gotten some good advice already. Prepare financially, figure out what your options as a military spouse are (I do know from a friend's experience that child support can be taken right out of his check before he even sees it, and the $$ gets sent directly to you), go to counselling to decide whether you want to take him back. In other words, take back your power.
Don't sit there worrying, wondering and crying. Take some active steps to insure your and your children's futures.