I guess for some it isn't just a kiss, it's a betrayal and given your scenario the only reason he admitted it was bc he was busted. So I would consider it that he was only remorseful he was caught not sorry he kissed her.
Would I end the marriage? initially probably not. But I think all trust would be gone and it would eat at the relationship and it would probably inevitably end bc I would be checking up on him and second guessing his every move. So even if it was only a one time mistake, my lack of trust would drive the final nail in the coffin.