Husband has no moral compass?

This is a long one. Sorry guys! First two paragraphs has the main points...

Without getting in to the gory details, my now-husband has emotionally hurt me in the past. He has lied to me and, while we were friends, simply didn't treat me on the caliber as other people. The most recent "thing" is that he stole money to pay for our wedding. He never told me and I discovered it while we were purchasing a house. Obviously, these things have really hurt me. We have been going to therapy for a few months.

We got in an emotionally charged fight (on my end anyway). Skipping the details, I asked him if he ever felt "bad". You know, when you do something wrong and you FEEL bad. Not because of the law or consequences, but because you don't feel good doing something. He said no. He said he knows if something is right or wrong. He won't do a specific thing because either he is afraid he will get caught or he has no urge to do so or he doesn't want the consequence (like someone would be hurt or yell at him) but no interal thing saying "this is wrong. I would feel bad"

He gave the example of if he were to leave a ring on the table at his parents house. If his mom questioned everyone and then proceeded to spend a half hour scrubbing it out. He said he honestly wouldn't feel bad and he probably wouldn't even think about it while he sat there watching his mom struggle.

Even the things he has done to me. He says he is sorry he did them because they caused me pain and hurt, but he doesn't feel a burden by them. He said if I told him tomorrow EVERYTHING is totally forgiven, he would probably never thing of the things again.

To redeem him, he said all of this crying. He said he was crying because he thought I would hate him or leave him. He also does "good things" because he doesn't want to hurt me by lying to me (although I think he would have no problem lying to others).

For example, that night we went out to dinner. He came out of the bathroom and he told me he piped on the toilet (it was longer and funnier than that). I asked if he cleaned it and he said "yes, because I knew you would ask and I didn't want to lie to you". I would never know, so that must be something, right!??

He's always kinda been like this, but I never put all the pieces together. His mom self proclaims she doesn't feel empathy and his brother is, well, a dick who never takes people into consideration. My therapist says have have a "very strong moral compass", so maybe there are a lot of people like my husband? Maybe he's a "normal guy" and I'm just too emotional?

Please give me your thoughts.