Jaime and Brienne do some more bonding in the bathtub. Jaime tells her some of his secrets: that he killed Aerys not only because Aerys was the kind of guy who thought boiling people in their armour was great entertainment, but because Aerys was planning to burn Kings Landing with wildfire. Jaime watched from Aerys' side as all the secret planning was done. When Tywin showed up with an army, having finally figured out who was going to win, and therefore whose side he should be on (this is why Ned moaned way back in book 1 chapter 1 about the Lannisters turning up late for the war), and Aerys instead of surrendering told Jaime to chop off his dad's head, that was the last straw.
So Jaime chose his dad over his king, punished his king for cruelty, and saved the entire city from a fiery death. He's quite the hero. Then again this is his POV so I guess it is all coloured by his opinion of himself...
Brienne and Jaime are summoned to Roose Bolton. Bolton plans to give Harrenhal to Vargo Hoat then head back to serve Robb. But he doesn't want to incur the wrath of Tywin, who might be a bit put out by the whole chopping off of his son's hand business, which he might blame on Bolton. So he gets Jaime to agree to tell Tywin that he is a top bloke, in return he frees Jaime and gives him a decent escort home. Brienne, on the other hand, is going to be handed over to Vargo. Is Jaime going to stand for that, now that they're best buddies (he's even stopped calling her Wench)?