I ought to clarify my comments on having a President from one party and a VP from another. I wasn’t referring to in a “normal” (whatever that is these days) election, but more a situation a la The West Wing where a sitting VP resigns/dies.
As far as I’m aware the new VP can be absolutely anyone chosen by the President under the 25th Amendment (yes I had to Google it!) but that the nomination must pass the House and Senate vote. Hence why “Bingo Bob” ends up as Bartlett’s VP when Haynes is forced to resign, because the Republicans refused to confirm any Democrat that was strong enough to contest a Presidential election.
They also refer to the idea of nominating Republican Arnie Vinick as VP for Democrat President-Elect Matt Santos when Leo McGarry dies on Election Night.
Sorry to keep referencing The West Wing, but it is my sole source of information on US politics 😂