Welcome to the forums. First of all, let me say I am so, so sorry about your illness. And I am so, so sorry for what your husband has done.
There will be other, more experiened veterans along shortly to help you. I can only offer my perspective, which is only an opinion.
Your husband has cheated on you. This is not polyamory. This is him attempting to cover his tracks and justify his deceipt, betrayal of trust, and total disregard for your feelings. And then he has the nerve to say if you ask him not to see her it will hurt him? I'm a little sick to my stomach right now, and I don't even know you guys.
But I've been cheated on before. It hurt. It hurt a lot. A lot of nights crying myself to sleep and wondering why. Losing 20 pounds because of a total loss of appetite. Depression medication. It took a lot of therapy and a lot of changing of behavior on my spouse's part to get through it.
Here is what I required of spouse: 1) No more contact. At all. Except an email to her affair partner (that I approved) saying not to contact her anymore. 2) Marriage counselling. 3) complete transparency for a time, including letting me access all emails, texts, etc. and letting me know where she is at all times. 4) Reading several books together with me our counsellor had picked out for us. 5) Answering any question I had about the details of the affair.
My spouse did all of these things, and our marriage improved. I also took the optional step of contacting the affair partner's fiance and letting her know everything I knew. We regained much of the trust that she had betrayed, improved our communication skills, and came out stronger.
Now, I'm not saying you should necessarily pursue my path. That's up to you. But if you want to salvage your marriage, don't even think of polyamory right now. That can only come after a stable relationship consisting of openness and honesty, and after many, many thoughtful discussions of bringing someone else into your lives. Do not let him rationalize his way out of his reprehensible behavior. Hold him responsible for his actions.
I'm not saying that you have been a perfect spouse, or can't do things to improve the relationship. We can all become better partners. But he alone is responsible for his choices.
Take care of yourself. Drink lots of water, try to sleep if you can, and please see a doctor if the feelings become overwhelming for you. And please, post here often. It's therapeutic.