Well, no, right now this isn't poly. But it could be. And if it evolves into a healthy poly relationship depends a great deal on you.
I have a great deal of sympathy for you and your husband. Yes, he has cheated repeatedly over the years. That is so hurtful. You have every right to be angry and distrustful.
But. And this is going to be hard to hear. He has apparently tried to tell you the truth about himself for many years. A truth that you did not or could not hear. One you denied and shut down. I understand why. Monogamy seems no normal, natural - and of course you have had no trouble being monogamous. It comes easily to you. And so it should be for everyone - not being monogamous is a sign of immaturity or lack of will power, and so on. Those are very common ideas in our culture.
Please understand that I am not condoning his cheating. That is not acceptable in any relationship that has a foundation of honesty. He should have tried harder to get you to understand. He should not have had affairs.
So now what? It is good that you came here, seeking information. You want to understand now. This is a hopeful for your marriage. However, now you have the difficult decision to decide if you can be in a poly or open relationship.
(The commonly accepted difference is that poly indicates that an non-monogamous person wants multiple loving relationships - including sex - while open indicates that the people in the open marriage are open to their partners having outside sexual partners - sometimes these evolve into relationships and thus poly but often not. There is also an overlap with swinging and open too. There is lots of conversations on the forum about the differences and overlap between poly, open and swinging.)
It is possible to have healthy, loving, honest relationships where one partner is poly and the other is monogamous. (Search on the forum for the tag 'mono/poly'.) It's possible but it's hard. Not everyone is suited for it, nor should they be expected to be. Take your time, learn and listen to your husband and your own heart. Ask questions, think about what you really want and what you can live with.
Your post reads that other than cheating, your life with your husband is good, fulfilling and loving. That is a strong foundation to build from, if you choose. It sounds like he wants to be honest with you, that he wants to stop cheating, and have open relationships with others, with your consent and knowledge. That is also, on the face of it, promising. It is possible to transition from cheating to honest, poly relationships. But again it is very hard and requires time and much long slogging to rebuild trust.
Cheating is obviously a moral failing. But it is also a pattern of behavior. Your husband might find it difficult to move away from those patterns - of not telling you the whole truth, of shading the information he tells, of outright lying and covering up what he is doing. And he is used to not being heard or accepted when he tells the truth. (Again, this is not to blame you or condoning his actions but it is a reality of the situation.) Honest relationships are hard and take work and can cause pain, unease, discomfort while getitng to a place of honesty and trust. It will be likely be easier in the short term for your husband to fall back on this usual ways of not telling you the truth when it's hard or when you are not hearing it right away. He is also going to have to do some serious shifting of entire behaviors and thoughts in order to make a honest, ethical poly relationship work with you.
Finally, marriage counseling is a good idea. However, I suggest you look for a counselor who is either poly friendly, open to the idea of ethical non-monogamy, or works with 'alternative' populations like LBGT folks. A therapist who is open to ethical non-monogamy will be better able to 'hear' your husband and maybe do some 'translating' back to you.
You have my best wishes.