I'm sorry that you find yourself struggling to understand your WS's logic and truthfulness. To be honest, trying to make sense of what is going on in the wayward mindset is a little like dropping a handful of wet spaghetti on the floor and trying to derive some meaning from how it landed and what shape it took. There is no logic to how wet noodles land on the floor, and that same lack of logic applies to WS's as well. You cannot make sense of something that never made sense to begin with. Sometimes a mess is just a mess.
To help you understand his thinking a little, lets talk about something other than infidelity for a moment. Let's talk about bodyweight instead. A lot of people struggle with their weight and their efforts to control it. For the purposes of this discussion, let's assume that "Mary" is overweight. Her weight makes her feel bad about herself. It makes her feel ugly, and unwanted, and she often feels that people judge her not only by her looks, but also judge how smart she is, or how helpful she is, or what her interests are, and assume that anyone at her weight is stupid, lazy and only interested in food. After many years of feeling that way, Mary now sees herself the same way. She can't find a date and that makes her feel worse. She needs an extender buckle on the airplane and that makes her feel worse. Every time she's reminded of how her weight is making her life awful, it adds to the way she defines her own self-worth (or in this case, the complete lack thereof). She then feels worthless and ugly and stupid, just like everyone says. Pretty soon, two things happen.
The first thing that happens is that Mary self-soothes herself by overeating. Now stop and ask yourself, if someone is fat, and hates being fat, why in the world would they go get a tub of ice cream and eat it when they feel bad? It makes no sense. The ice cream is only going to make her fatter, right? But when we are hurting and traumatized, our brains don't think so logically. In fact, our brains often think in very illogical ways instead when we're hurting. Mary hates herself for being fat and hates herself more for grabbing the tub of ice cream and eating her feelings. But she does it anyway. She does it because the ice cream distracts her and makes her feel better for the moment. Bear in mind that we don't have to be talking about the world's best ice cream. If we are sad enough, we will eat crappy, grainy ice cream from 7-11 and hate every bite of it, but finish the tub anyway. And once we finish the tub, do we feel better? No, we feel even worse. And so we go buy more ice cream.
The comparison I'm trying to make here is that your husband could have felt gross and dirty for being with the AP, but still gone through the steps of what a relationship should look like with her, because that's his role to play in order to get what he wants. Ice cream is paid for in cash. The store needs cash, you need ice cream, and so a business arrangement is made. Each side gets what it needs from the other, as long as everyone plays their part. Infidelity is similar. Your husband needs to feel special, wanted, attractive, and desired. The AP is willing to fulfill those needs from him, but she has her own needs. She needs to feel special and wanted as well, attractive, and desired. So in order to get what he needs from her, your husband had to pay her price, which is to fill her needs. It has nothing to do with love or even feelings, and everything to do with getting needs met while trying to convince yourself that you're not a bad person in the process.
The thing is, socially speaking, making someone else feel special and attractive takes on a certain shape and behavior. Saying, "Hey asshole, you look pretty today" doesn't work. You have to fulfill the social norms and play the game. So instead you say, "Gosh, you're so pretty, you're my everything!". You don't have to mean it. You just have to say it. That's your role in the relationship, and it is how you entice the other person to respond in kind. The other benefit of all this "lovey-dovey" talk is that it helps the cheater to lie to themselves. Cheating is a gross and dirty business. It makes you feel awful. But you know what? If you allow yourself to believe the lie, and just tell yourself that your AP actually MEANS those lovely things they are saying to you, then you take some value and solace from that. Think of it as moving into the ice cream store so that you always have a full supply. You are still fat and gross and eating your feelings, but you don't care because you've set yourself up with a way to feel good anyway, even if it's artificial.
The second thing that happens is that Mary loses the ability to love or respect herself, and so she relies on the approval of others to make her feel good. Self-love is like oxygen. We need it to live and function. When we don't have it... well, it literally feels as if we are going to die. People who can't breathe will do ANYTHING to get air, and people who can't love themselves will do anything to get love from others. This state of mind can work out just fine for years and years for many people. But when things get tough and that supply of external love and validation begins to wane, the person falls apart instead. To be clear, I don't mean that they "get sad" or "feel lonely". That's what normal people do and feel, but most people love themselves to begin with and so they can recover and grow despite a lack of external approval. But a person who can't love themselves instead goes into a panic, and from there, to a place that I can only describe as "very dark and not completely sane".
Since they cannot love or sooth themselves, they instead choose to blame others for their anger and loss and hurt. It's their spouse's fault for not loving them enough. It's their family's fault for not being there enough for them. They find themselves hurting to the core and desperate to feel good, so they convince themselves that anything they need to do is justified somehow. If someone is starving, they might have to justify stealing a loaf of bread, and then blaming the people they stole the bread from for not giving it to them in the first place. That's how the WS mind works. They blame the people they hurt for their own pain, but because they can't value themselves, they also can't take accountability for themselves, so they double down on their pain being due to everyone but themselves.
Anyway, my long-winded response is merely to tell you this... you already know that your WS is lying (or has lied) to you. I think it is a misstep however to assume that he was "telling the truth" during the A. A liar is a liar is liar, and as long as he's a liar, then he was lying to everyone, including you, including the AP, and including himself. So if you can, try to stop seeing what he did during the A as "the truth" and see it instead as "more of the same lie, just told to someone else".
One last thing. None of this should ever be used as an excuse or justification for infidelity. Rather, by understanding what factors led up to it, it gives us choices about how to move forward, and it offers the WS a "first step" towards recovery if they can accept it and own it. We can't change what was. But we can gather the knowledge and tools we need to be better people in the future.