By default, you can play as Cuphead and Mugman (or Ms. Chalice with the DLC) on the same system.
Although does not officially support online multiplayer, players have developed several highly effective workarounds to play with friends remotely. Officially, the game is designed strictly for local co-op only. Official Multiplayer Status Cuphead online
There is no official "online" menu or matchmaking within the game itself. By default, you can play as Cuphead and Mugman (or Ms