I actually fixed it and got it working. Turns out I had to configure the WAN interface on the host side.
My /etc/network/interaces file now looks like this:
# This file describes the network interfaces available on your system
# and how to activate them. For more information, see interfaces(5).
# The loopback network interface
iface lo inet loopback
# The primary network interface
iface eth0 inet static
iface eth0:1 inet static
# The WAN interface
iface eth1 inet static