Sorry, this is going to be long.
I know this isn't exactly the perspective you were asking for, but I want to speak from the point of view of the baby in this situation.
My parents had only been going out with each other a short while before my mother got pregnant unplanned.
My father announced that he was willing to keep seeing my mother up to the point that the baby was born, after which he wanted no contact with her or the child.
Unsurprisingly my mother said that their relationship was over.
True to his word, my father refused to have anything to do with me, despite my mother making it crystal clear that he was welcome to be a part of my life.
While my mother was pregnant he got together with another lady who eventually became his wife. They didn't have children together.
I wrote to him when I was six, got no reply.
I wrote when I was fourteen, telling him a bit about myself, asking for a photo (my mother had never had one of him to show me). I didn't ask to meet him. He replied to my mother, requesting that she 'discourage any further communication'. Oh, and no photo.
Make no mistake, I had an immensely happy, safe and loving childhood, and I could not have imagined a better one. My mother was always open and reasonable about what had happened and supportive of me in how I dealt with my feelings. In most practical ways his absence was not an issue.
BUT. The fact that my father wanted nothing to do with me has caused me terrible terrible unhappiness at times. I grew up with a void where my paternal background should have been. No information about my father's family history. No stories about the past. No sense of what he was really like as a person. No roots on that side.
I don't know how to convey eloquently enough how much it hurt.
Those who grow up knowing their parents can only try to imagine what's like to have a great big yawning hole where one of them should be.
It's not the same as having a parent who died. His decision to reject me made all the difference. It has partly shaped who I am, and the way I approach life. It has wrung me out. I know some of the things that will tear that little one up when he or she is old enough to understand, and I feel so sorry for the child.
It has been one of the greatest challenges of my life to find a way to live alongside it and be at peace with it, and I am happy to say that at last I have. It took the best part of thirty years. I have had to work hard at it, just as I am sure you have had to work hard at forgiving him.
Now, some may (and do) say that they don't understand feeling like that - it's silly when he's obviously not worth it, etc etc. Fair enough, you don't have to understand it. You just have to believe me when I say that's how it is.
Whatever the OW did, whoever's to blame for it, that baby is as much of an innocent victim as you are. And believe me - he/she will have to suffer because of what's happened, just like you have.
Are you going to tell your children that they have a half-sibling?
What happens when this child grows up and knocks on your door looking for some answers?
Obviously, I have no idea what my father's life was like or what his marriage was like. All I know (without going into how I know as it will make this twice as long!) is that they had no children and that she has a great deal of resentment towards me.
I honestly from the depths of my being do not think it is fair, right, wise or kind for your DH not to have contact with his child.
I also don't believe that it's the right thing for him, you or your relationship, but I guess I could be biased . . .