Well I guess what I am saying...is that if he insists on having his fun too, then you need to release him so that he can do it. But him doing it while supposedly trying to reconcile with you is only going to damage the relationship further.
At this point, honey, since you've had an affair...I would think that another difficult conversation wouldn't be that big of a deal at this point....you've already weathered through a very difficult, painful thing and you lived through it...so how about saying: "husband, I am sorry that I snooped, but I did, and I can see that you have been texting with someone else and that you have a profile on an online dating site. I know I told you that you could have a revenge affair if you needed to, and that looks like what you are doing. However, I underestimated how difficult it would be for me to sit back and watch it happen, so I would ask that if you are going to go through this, we get separated first".
I know this isn't what you really want...but please don't kid yourself into thinking that if you just sit back and allow it to happen, he will then feel "better" and fix the marriage with you. It is unlikely to happen that way, dear.