Apache automatically listens on all available IP addresses (so network interfaces), unless configured not to.
In truth, you are very unlikely to get any benefit at all from multiple NICs, especially if one is part of the mainboard. The chances of just the NIC failing on it's own are very low (none if a NIC is part of the mainboard). You are unlikely to be able to saturate a 100 Mbps interface unless it serves very large files and/or has very large numbers of simultaneous connections. All NICs are attached to the same (PCI) bus on a standard system, as well.
I think that the better solution to the issues you're mentioned are to have multiple boxes and use a round-robin DNS entry to split the traffic between them. The base line spec for Web serving is literally a 486, so the boxes can be as big or small as you like. A simple script can keep the files on multiple servers identical.