Looks like you can only bind MySQL to 0, 1 or all interfaces on a system (MySQL: Bind to more than one IP address?)
You could try having MySQL bind to all interfaces on your server, configure a private IP space for the two directly connected NICs and configure MySQL to replicate using those private IP addresses.
Server 1 (Master):
NIC1 - 192.168.0.10 <- General access to server (connected to switch)
NIC2 - 10.0.0.10 <- Replication interface (directly connected to NIC2 on Server 2)
Server 2 (Secondary):
NIC1 - 192.168.0.11 <- General access to server (connected to switch)
NIC2 - 10.0.0.11 <- Replication interface (directly connected to NIC2 on Server 1)
Configure replication using the 10.0.0.x IP addresses and see if it works.
You can verify replication is occuring over the replication interfaces by using tcpdump to capture packets or checking the interface statistics for NIC2 using ifconfig.