Cheated on and not sure what to do

It has been a crazy month and a worse 24 hours. Yesterday I found a very graphic letter under the floor mats of my husbands truck confirming an affair with a woman he swore to me he was just friends with. We have been married for 9 years and have an 8 year old daughter. In april I had a little girl that we gave up to my sister and her partner as neither of us really wanted or could care for more kids.After that I will admit I closed off to him and everyone else. He has said it is over and that he doesn't want out of the marriage, neither do I at least in my heart, but I so want to confront the girl - 15 years younger than me blond and from her writing style very blond. He still sees her at work and has actually taken my daughter out with them as a chaprone a few times since he said that the affair ended. I am afraid if I put my foot down on the friendship that I will lose him. Is it possible to be just friends after a physical relationship of a few weeks (according to him) or am I being stupid? Don't want to push him out the door when he says I have given him no reason to leave and that he knows he *&^%*ed up and he is sorry he hurt me. He offered no excuses other than he was wrong and when he did try and justify he quickly corrected himself that it was not an excuse. Any thoughts???