second eth interfaces for VM
i'm running a similar setup, where all proxmox hosts are connected with two independent NICs and networks.
Code:

eth0 -> vmbr0 = external network
eth1 -> vmbr1 = storage network

so it basically looks like your setup.
for my KVM machines i can add virtual ethernet hardware and assign two virtual NICs to the bridges with the web-gui.

for my OpenVZ machines this can't be done with the web-gui (feature request). so i've configured 2 veth devices by hand. and added them do my /etc/vz/conf/<VID>.conf while the container was stopped.

Code:

NETIF="ifname=eth0,bridge=vmbr0,mac=00:00:00:01:09:00,host_ifname=veth109.0,host_mac=00:01:00:01:09:00;ifname=eth1,bridge=vmbr1,mac=00:00:00:01:09:01,host_ifname=veth109.1,host_mac=00:01:00:01:09:01"

that way eth0 of the host and VM are connected as
well as eth1 of the host and VM are connected.

network config of the VM is done inside of it with the means of your distribution.