WS's are fundamentally broken people. For whatever reasons, and every story is unique, they lack the basic skills and norms of healthier individuals. Imagine the kind of person it takes to have an affair in the first place. They clearly do not love or respect themselves to begin with... people who have integrity and dignity don't lower themselves to such an act, they could barely conceive of it. They also lack the ability to "actually" love other people. Their love is transactional in nature, and it is measured by how others make them feel about themselves. They do not love themselves and so it makes them incapable of loving others. Most WS's also have a tendency towards addictive personalities as well. Some are obvious such as abusing drugs or alcohol, but others are more subtle, for example, having poor spending habits and developing ways to cover it up.
The real problem with WS's however is simply the fact that most WS's have absolutely no idea that anything at all is wrong with them, and are often just as shocked as everyone else to find themselves in an affair. Since WS's do not love themselves, they cannot bring themselves to face the things they are doing (you can't self-criticize when you have no self-respect to begin with) so their minds turn to justifications and excuses to try to alleviate the guilt and instead misdirect it towards their partners, or ignore it altogether. Not surprisingly, this exacerbates the problem exponentially. Someone who is incapable of self-love goes off and does something really horrible such as an affair, which in turn only makes them feel even shittier about themselves, which makes them hurt more inside, and so they go and look for another way to relieve that inner self-loathing... it becomes a vicious cycle of lying to themselves, then to others, and eventually, losing sight and understanding of what "the truth" is in the first place. It would be incredibly sad (and it is) if it weren't so damn toxic to everyone around them. If they were just alcoholics their loved ones would rally around them and have an intervention. But when you are busy lying to and betraying everyone in your life without owning that, and without remorse... well, you just killed off your only real support system.
Take it from a WS who has spent the last 7+ years struggling to crawl out of that pit. It takes a lot. It takes a lot of work, for sure, but even before that, there has to be a willingness to DO that work, to dig deep despite how scary that is, to admit and to look for flaws in themselves, and take on the weight of both all the damage they did to others, and all the damage that was done to them in the first place (which is how they ended up this way). It's no surprise that most people would rather stay in la-la-land and not face the ugliness inside of them, and not face the struggle and pain that it takes to become someone better.
I see you registered here in 2018, so... this is not something new. Granted, it does take some WS's quite some time to get their head out of their ass... it took me 3-4 years to even get to a point where I could understand all this and so be able to move forward, and that was with me actually doing the work and wanting to get better. But it sounds as if your WS hasn't been putting in that effort. It sounds like he is still rug-sweeping, minimizing, and avoiding... which in plain English means he's not doing anything to change. As Brene Brown puts it, he is "hustling for his own worth" every day, but it's just a hustle, so no real change or growth can come from it.
FWIW, my wife always says that people don't change until forced to, and I find that true. If your husband isn't doing the work, then he remains an unsafe partner to be with, because the things in his flawed character that allowed him to cheat in the first place... are still there, unfixed and un-dealt-with. I can't really advise you how to approach that, but I can let you know that "when nothing changes, then nothing changes". He hasn't changed, and he isn't be forced to change, so he remains the same. Clearly, the consequences he has suffered so far are something he is able to handle, and it hasn't been enough to motivate him to take a different road. Either that, or he is too broken to do so, but the end result is the same. He remains a danger to himself and you, as well as others in his sphere of influence.
If I can recommend anything at all, it is this. Put down healthy boundaries. If he's not in IC then he needs to be, and if he isn't, it's time to leave. There needs to be effort, and progress. (Progress ebbs and flows but it should be positive over time). If there isn't effort, then it's time to leave. Figure out what it is you need from him (other BS's can be helpful in this regard) in order to be safe and in order to consider staying. Enforce those boundaries. Put in timelines or conditions. Either he steps up to the challenge, or he doesn't. Either way, you'll know what you are doing and why.
I wish you both luck.