Richard and Karen Carpenter, though only recognized in Arkansas...
(I am aware they were siblings. Same for Nino Tempo and April Stevens.)
The Captain and Tennille come to mind. Steve Lawrence and Eydie Gorme. Paul and Linda McCartney, but calling her a musician was pushing the envelope. She was the Lucy Ricardo to his Ricky. Same with John and Yoko. She was a wannabe.
And there were two couples in Fleetwood Mac. For a while. Mama Michelle Phillips and Papa John Phillips were married. Debbie Harry and Chris Stein in Blondie. Tina Weymouth and Chris Frantz from both Talking Heads and Tom Tom Club. Gloria and Emilio Estefan. And I'm sure there are more in some indie bands nobody ever heard of.