Each card will have it's own IP, but most webservers default to "all" addresses, and it's actually a bit of a pain to disable it for IIS.
Inbound, connectivity depends on which address the remote machine is talking to. If you have 192.168.1.1, and 192.168.1.2, and 192.168.1.1 goes down, then traffic that is intended for 192.168.1.1 will not go through.
Outbound, the server should use whichever interface it deems appropriate. You can type
route print to see how it's set up, but it should automatically failover, unless you've crippled connectivity somehow on the second interface.