Well PW, I think he is ashamed of what he has done and because he is living under the same roof. He still doesn't want to look like the bad one.

Mine just now admits to his other woman openly because it is over. Even though he didn't live in the same house, and even though he knows I am with someone else he still couldn't freely say her name or admit to his trips to see her. He has only just told me how he felt so ashamed and bad as a husband and man for what he has done.
He kicked her out of his place and somehow I think this freed him to be okay with himself because for once he could say there is no one else and not be lying.

Your husband is still lying and he knows this and all that he has done is wrong. He is not good with himself so he can't be clean with you.