Wow. I'm sorry to find that you are here, especially at what is supposed to be such a joyous occasion, a new addition to your family. Congratulations on the son! The most important aspect is that you do what you need to do in order to protect yourself and by extension your son and to give yourself some grace, and if that means you need to ask friends or family for some help with a new baby, do so!
As far as your husband, wow, in some ways, I can relate a little bit. My wife and I got engaged in Dec 2009 and later that same month, I was hanging with some friends, drinking and partying, but I ended up sleeping with someone while my fiancé (now wife) was out of the country on holiday that year (my wife is from outside the USA). Suffice it say, when she returned in January, within one day of being home with me, she found the chat logs of me discussing the whole thing with this woman and confronted me when I got home. This was years before we would find SI, but she did all the things that we insist a BS do, go no contact and be fully transparent. I was about to lose her, our engagement at that point was on-hiatus or off completely. She didn't have any place else she could reasonably go at that time, as she was an international student living with me, but we did sleep separate for a bit there. Eventually, through the course of things, we began looking at trying to fix the relationship and reconciling. A few weeks later in February, we went out for dinner and drinks at one of our favorite places after my workday. Over dinner she proceeds to tell me that she is a few weeks late and thinks she may be pregnant. She took some over the counter tests later that night and the next day we got her an official test and she was pregnant. The topic of reconciliation and recovery suddenly became an afterthought to both us as we were about to become parents.
Because of her student visa status and protecting her and the baby, we opted to have a small private ceremony with my family and her sister who lived in town and we got married on May 01, 2010. I say protecting her because we needed to get her and the baby on my health insurance and there was no other option for affordable care. 13 or so years later and additional infidelity by both of us, we have since recognized that if not for that pregnancy in Feb 2010, it is quite likely that we never end up staying together. It hurts to realize that, because I do love my wife more than anything today, as reconciliation has been slower for us, but we have gotten to a good point in our relationship, she has been with me through quite a journey since then, and I wouldn't do it with any other person.
So back to your husband, you can see how I recognize a bit of myself in your post about him. It took me a long time to get my shit together and get serious about addressing my past infidelities and doing the work to affair proof myself going forward. He has to earn the right to be with you going forward. He has to show you through his actions and over the longer term that he is committed to you and your new family. He does that by finding the right therapist to hold his feet to the fire and own his shit. He does that by committing himself to total honesty and transparency. No little white lies, no matter how small. I'll give an example of the lies I'm talking about, if I'm having a conversation about something and there is a specific detail like a number, let's say the number is 34 but that specific detail escapes me, I will be honest and say, I know the number is in the 20s or 30s, but I don't remember specifically how many, and someone will provide me the correct detail of 34. I do that because the old me would've acted like I knew the answer all along and had said a number only to be corrected later. I guess it's hard to give that example, as it is specific to my work life, and a conversation I had earlier today, but I've found that for my memory, specific figures elude me a lot, but general ballpark numbers I can remember or sometimes those figures never get to my memory. But, my commitment to being honest and transparent in all aspects of my life is a change that I'm committed to doing, because when I tell the truth at all times to everyone, it is quite a freeing feeling to not have to worry about what little fib I told to this person or that person, and believe me, looking back on it, I would tell all sorts of little fibs about all sorts of totally bullshit things to make myself sound more likeable, or cooler, or whatever vanity reason I thought justified the telling of that lie.
I guess my message was that, if your WH is serious about getting help, and again, like an addict, the user has to want to get help, you can't force them to go to rehab, just you can't force your WH to do anything. What you can do though is enforce boundaries that you set. If you set a boundary that he not engage with any women on social media, texts or email without you knowing about it, and he violates that, you have to be ready to take action and enforce that boundary, up to and including a divorce. But, if your WH works on fixing his shit he can one day again become a safe partner for you or for someone else, however your marriage shakes out.