I think arguing whether the relationship is a 'good' one is silly.
But most who find out their partner has cheated do honestly believe they are in a good relationship. Partly because that is what the cheating partner wants them to believe too - and will often do things to make sure it appears that way too.
BUT there is only a relationship if both sides are giving to it equally.
It is only later when real communication begins that the relationship can be examined.
My h will accept that there was 'nothing wrong in our relationship' and that it was fault in him.
However I do think that i too had become complacent in our marriage.
What will give the op real strength is to know that she could cope as a single mum and that the only reason she is staying is because she WANTS to and not because she feels she can not cope alone.
Cheating is not something that 'just happens' either - the person has to accept that they are a cheat and have to learn how to deal with that.
It is not just a case of forgiving either - I have had to accept that my h was/is a cheat (he will never be able to take away what he did).
But I know i have the strength to survive with or without him and be happy whatever the future brings.
OP it will be hard and you have to accept that things will never be the same as before - never be the way you may have dreamed or wished. But that does not mean it can not still be fantastic.
You can recover from this (and worse) and it can be in so many ways better than the old relationship you had.
And does it matter whether it really was a happy marriage - that is now gone and your own perception is what really matters anyway.
If your h is willing to work together with you it can work out.