Any girl whose FB picture is of her butt is a skank IMO. It sounds like your husband definitely had a huge lapse of judgment, to say the least. He may not be used to being married yet, but if you and he were in an exclusive relationship before getting married, he should have already known that talking to skanky girls on FB was NOT appropriate in any way.
You need to sit down and have a heart to heart with him. Tell him that you feel like he only deleted her etc. because he got caught- if you had never seen that message, he was encouraging this girl to keep in touch and contact him again!! He needs to do more than just mope and say he didn't mean it.
He has betrayed both your trust and the trust of your marriage, even if nothing happened. Online, this is exactly how things START to happen, even if he doesn't have that specific intention. You should not get married if you expect to keep hitting on girls, even virtually. Explain to your husband that this is just the same as if he was hitting on a girl in a bar. Ask him how he would have felt if he had checked YOUR FB page and found you talking to another man that way??
When you have a spat, (and you WILL, it is bound to happen) you and he MUST talk it out. There is truth to the saying 'don't let the sun rise on your anger'. You need to agree to disagree sometimes, but you have to clear the air and know that your love for one another is so much more important than any temporary disagreement if your marriage is to be successful.
Ask your husband why his reaction to an arguement with you was to talk to another woman? After all, he could have gone out with some guy friends for a beer, called his dad for advice,gone fishing or played a video game- there are so many other ways he could have diffused his feelings that do NOT involve other women.
This is not a deal-breaker to your new marriage. But if this kind of thing continues, it definitely would be for me. You need to talk this out, set FIRM boundaries that both of you will stick to about interacting with the opposite sex and- this comes from someone whose ex-husband had a SERIOUS internet addiction- your husband needs to realize that meeting someone online who flirts with you is not any 'safer' or different from meeting her in a bar! He needs to understand that you and your little family are his priority now and man up when you have a disagreement!
Good luck!