When Hester finallly tells Dimmesdale about Chillingworth's true identity, Dimmesdale runs the gammot of human emotion. He initially does not handle it well at all. When she first introduces the name of the man who is her husband, Chapter 17 says, "Never was there a blacker or a fiercer frown than Hester now encountered."
This angry posturing doesn't last long, though. He soon falls to his knees on the forest floor, saying he should have known it and felt it in his guts all along. He then follows this by blaming Hester for allowing him to be in so much pain and in the clutches of the enemy for so long, just by keeping her silence. This drives Hester near madness. She can handle anything but Dimmesdale's disapproval. She holds the weakened, sickly man as a hug-hostage until he finally forgives her.
Dimmesdale finally realizes that, although he is plagued with guilt, he finally knows someone whose sins are worse than his own - Chillingworth. He and Hester face their lowest low, but they face it together.