Reviewed by Ian MacDonald, in Revolution in the Head:

TWO OF US (or 'On Our Way Home' as it was called during recording) was, despite its early-sounding simplicity and Lennon's later claim of authorship, a new McCartney song. Supposedly about his relationship with Linda Eastman, the words of its jogging G major verse/chorus fit - they liked to drive out into the country and 'get lost' for a few hours - but, when the key jumps unexpectedly to wistful B-flat for its 6-bar middle, the lyric seems to be more to do with John and Paul than Paul and Linda. (The lines about 'chasing paper' and 'getting nowhere' are usually taken to refer to the Beatles' contractual troubles, which escalated into a full-blown lawsuit two days after the 'Get Back' sessions ended.) The close harmonies of TWO OF US reminded McCartney and Lennon of their teenage Everly Brothers impersonations and, during the second day's work on it, they broke off to sing 'Bye Bye Love'.