I don't think either Frank or the Dead covered EVERY Beatle song, but they did a select few.....
Sinatra did a mean version of "Why Don't We Do It in the Road" on his Stoned Sinatra Picnic LP in '69! ;>)
I don't recall the Dead covering many Beatles songs.
Garcia did an intense Dear Prudence, and "I Saw Her Standing There" on his solo album; they covered the reprise of Jude in a segue from Dear Mr. Fantasy (Traffic). Later on they covered Lucy. Can't think of too many others. They probably covered more Dylan tunes than anyone else,though.