itsHunkyDory I really and honestly understand your predicament because we have just gone through 4 years of sheer hell with my DS(18).
My DH has been a great stepdad to him but DS had issues related to a lack of relationship with his real father not wanting to know him. This caused anger issues, bitterness and resentment towards our other children who DH is a natural father to. Even though DH worked tirelessly and really hard with DS there were times in the deep of night when DH would ask if he was cut out for the role of a step parent. It is hard, hard work and totally thankless but DH was not sure he was doing things correctly.
We both have had many meetings at DS's secondary school about attitude and attendance but never, ever got involved with SS.
Whilst everyone says that he is your son and must stay with you it does not detract from the emotional difficulty you face in trying to mediate between everyone in your home.
However your DH needs to understand that your son clearly has some kind of underlying emotional issues which cause him to flare up at home (perhaps seeing your DH playing happy families with your other children as my DS once said) and cause problems elsewhere with authority.
As difficult as it is and if you want to keep your marriage and family intact, you have to make your DH understand that his approach is all wrong and you need to find another way, together as a family, to help DS feel happier and thereby creating a calmer space at home.
We are still going through it with my DS but I would refuse to make a choice if ever put in that position. If your DH wants to leave then let him but it would be his choice, not your choice that you were forced to make. I think your DH making that demand of you is more an indication of his frustration at the situation rather than not caring at all for your DS.
Sometimes we, as mums, have to take control of everyone in the house and manage the situation until we get it where it needs to be. If you think your marriage can survive it then you need to take control and explore other avenues. There is no reason why you should lose your DS or your marriage. Most families have these situations with teens who live with both their natural parents so it is nothing usual.
If it were us the first thing we would do would be to allocate some regular one on one time with your DS, getting to know what he likes and dislikes, who his friends are, what his aspirations are hopefully from there it will lead into a conversation of how he feels and why. When you have that information then you will be able to source the correct answer to help him feel better.
Hang in there, seriously. Marriage and children are lifelong, heavy commitments and it's only natural that you should feel the burden every so often but that does not mean it is not fixable. Firstly you have to talk to your DS and get his take on things. (Tip, do not allow him to manipulate you because some of this is about control over you by him, likewise with your DH.)
Good luck.