Is it possible to play the PC version of Left 4 Dead 2 in split-screen, where one player uses the mouse/keyboard and the other uses a gamepad?
Yes, you can. You have to make sure you know your way around the console, and playing online might or might not work.
Basically, you have to enter these commands in the console to make it work:
ss_enable 1 ss_map "map_name" connect_splitscreen localhost
You have to make sure your Xbox 360 controller is set up correctly, for that, read this forum post: Left 4 Dead: SplitScreen PC Guide.
It's possible play split screen with a non-Xbox 360 controller, but you'll need to set up your own controller configurations by editing edit \left4dead\cfg\360controller.cfg. The lines you'll need to edit are the ones starting with "cmd2 bind".