Mou, I feel so sad for you and your son. I agree with other posters that your son's behaviour is highly likely to be caused by feeling unwanted, unimportant, not listened to, not loved for the person he is etc. Even if DS hadn't heard the conversation - which is devastating for him and will probably affect him for life, if this is how your H feels then it will come accross to DS through his mannerisms and the way he talks to him anyway. It is not good for him to be around your H the way he is now.
If your H could get professional help and could really change and could then make it really clear to DS that he does love him and want him, he was just ill when he said those things, and keep reassuring him and making it up to him then this would be the ideal thing. Could this happen/is it likely? If this is not going to happen then it seems like the best thing is to leave your H.
Your son needs you more than your H and is more vulnerable. It is your responsibility to protect your son however scary that is, and I know it is scary. If you don't protect him and you put your H's feelings above his and your own feelings above his(because it will be very hard for you to lose your H and I acknowledge that), your son will never truly forgive you and will be very damaged. You will probably never forgive yourself!
So, if you think your H can change enough, get him some help and support him in coming to terms with what has made him the way he is. If you don't think your H can change enough to make your son feel totally reassured then leave him. It may be the hardest thing you ever did but after the worst is over you will know for the rest of your life that you did the right thing and you were very strong. If you take the easy option now to protect yourself and leave your vulnerable son open to abuse you will feel bad about it for the rest of your life.
I'm sorry if I sound harsh but this is emotive for me as my mum took the easy option of not protecting me from abuse and I am still messed up at the age of 36 and my relationship with parents is irreversibly damaged.