I think because the parents just heard about the news, it takes some time for them to get through the initial reaction. Just like when we got the bomb. Plus, you are the daughter which I am sure have a special place in your parents heart. I did not tell my parents because I am so worried about my dad's health and my mom's reaction if she knows. Even if we reconcile, she will for sure be complaining about him forever. Right now they think my H is always the great SIL. The only relatives who know are my MIL (who was visiting us when I found out so I cannot hide it from her, but she does not know the details) and one of H's sister. Both are supportive of me. H's sister who knows that H is still contacting OW said she is sad that H is hurting me so much. She is actually surprised why I moved with him given the situation. This is the difference between those of us who went through this and those who have a lovely family. Before A, most will think if there is an A, it's over. Now we think otherwise.
Your H just can't live without you. He thinks since he loves OW, and he will love you as DD's mom or a great friend. Perfect scenario. Does not work that way....