Well, if he is still at home and texting/calling his affair (and don't buy the line that they are just friends and it's only an emotional connection because I would be willing to bet that is untrue) then set your boundaries.
H, if you choose to live in our home I will not tolerate you texting/IM'ing or calling another woman in our home, in front of me or around our children. If you cannot respect this boundary of mine then it's time for us to come up with different living arrangements at once.
Then say no more. Do not engage in further talk/conflict or tit for tat about this matter. Your boundary and decision is final and that is that. He can choose what he wants to do and if he can't choose to at least respect your boundary then make it simple and choose for him.
My motto is always "go hardcore with compassion but do so with SELF respect".
I am so damn sick and tired of reading thread after thread where the LBS lets the WAS walk all over them, flip their life upside down, hurt children, ruin finances, lie and essentially treat their partners like they are second class citizens and nobody does a thing about it.