After they defeated Higuchi, Light touches the rulebook and temporarily regains his memories so he kills Higuchi and assumes ownership of it, thus permanently regain his memories.

Why did light get his memories back but not MISA?

It is revealed that Light had planned the entire thing: the notebook Higuchi used was Light's original Death Note, with Light having made it so that Rem owned that Death Note and he forfeited Misa's while in confinement, thereby allowing him to gain all of his original memories.

Why did light switch the death notes?

Light needed his notebook to be the one that was recovered so he could write someone's name quickly and get his memories restored fully.