I've had several discussions with H and I decided he can come and live in the spare room in the apartment, at least for the time being. I told him that him coming back to live with us doesn't mean that we are back together and he agreed that he will only be there to help out with son and pre-baby stuff.
My son initially had a strong reaction by telling H to go away, but I think he is used to it now.
I know at face value it looks like a bad decision, but financially and practically it is challenging for him (and us) to get his own place, but ideally this is what I prefer. I thought as well that it might be easier to have him around to help me before and just after the birth. I also have a gut feeling that it will be ok. I know I don't want to pursue anything with him. I am lucky that the apartment is quite big and we have the space to mostly keep away from each other.