I've had multiple NICs for host servers, where there will be several virtual servers running inside. I can assign separate nics to individual servers and improve network performance this way.
I've also seen multiple NICs in a fail-over situation, where the switch port for one nic is disabled, but can come online automatically if a failure is sensed in the other connection.
I have a server with one NIC facing the external network, another facing the internal network, and another facing a dmz, but this server is my gateway and firewall. It does things like virus protection at the edge for the rest of our internal network. It is not my domain controller.
I have not seen a DC placed on the public internet, but maybe I've just lived a sheltered life.