I'd say you should each book one night. Check out of his reservation and check into yours. I doubt any other method (like asking nicely for a one-off) will be successful.

You would each get half the points, and you'd each get a full 'stay'. If you choose points + miles, you'd also both get the full amount of miles for a stay.

If the reservation is already made, then see if you can book the second night under your name. You can always specify a shorter check-out for your reservation when he checks in.