E, looks like you did an amazing job to me. I had to have a similar discussion with my H, but was a more than just bringing a "friend" into our house and we have no children. I was very calm and collected, but stern at same time. The major difference is in how your H responded. He was not defensive at all and apologized straight away. This IMO shows that there is very likely nothing more going on and she is just a friend.
My H was contemptuous, defensive, and argumentative and got into semantics of sleeping with someone vs. female friend. This told me all I needed to know to confirm my worst fears. He feels he can do the later. Yes, ok, I did not argue with that.
Anyhow, great work!!
Me: 42 H: 40 M: 12 H moved out - 8/2015 I filed - 8/2015