Hello OP.
There seem to me a lot of knee-jerk reactions here which you seem able to rise above, so you are already in a good place to gradually process, in your own time, this devastating betrayal.
I say that not to understate the huge impact of your H's infidelity, but in recognition of its (sad and unfortunate) place where it now sits in the long history of your relationship.
The first question for you, which I think you've answered already, is what do you want? What outcome? From what you've posted I think you love this man and value the family life you share.
I stayed. I am 16 years past that great chasm. It was a long and painful road to where we are today, only made possible by my commitment to my commitment (because I loved him, and above all I wanted my children's secure family life to continue), together with his genuine, heartfelt, utterly convincing regret at what was really nothing more than a cliched midlife crisis.
It sounds like your H is equally remorseful, and was immediately, which helps now and will continue to help you over time.
Over the next few months and years he needs to be consistent - in demonstrating to you that he understands the enormous hurt he has caused (this is crucial, his empathy for the pain he has caused) and also he needs to explore why he strayed - what weakness in him led him to seek to have his ego boosted outside the marriage.
I'm not sure couples counselling necessarily helps. For example, Relate seem to emphasise the mutual responsibility for infidelity. In my experience, and that of many others, that take on things is simply not true and can be really unfair to the betrayed partner - seeking to apportion blame where no blame lies. Sometimes it really is down to out of character feelings of insecurity that have arisen out of the blue (mid-life crisis) within the individual that has strayed.
One thing I am certain of is that what my H did was genuinely out of character. He was going through a strange time of stress and lack of sleep through long hours travelling to work. He wasn't thinking straight and instead of trusting me with his dark state of mind, he wrongly sought refuge elsewhere. It wasn't about me or our marriage, it was about his inner childhood demons that rose up in mid-life.
I don't know if any of this helps you, but I know for sure that my H will never betray me ever again and he is genuinely sorry for the hurt he caused during what was a whirlwind mental aberration. He looks back on that time like it was another person in his skin. He can't believe it of himself, and really, looking back at him before that time, and ever since, neither can I.