How is resolv.conf maintained when there are two network cards?

I have a Debian Wheezy VMware virtual machine guest with two network cards. One is in bridged mode and has access to the internet. The other is in host-only mode and does not. Some process, perhaps dhclient, is writing and overwriting /etc/resolv.conf. Sometimes it's written with nameservers for the bridged network. Other times it's written with nameservers for the host-only network. When it's written with nameservers for the host-only network it seems like VMware does not forward/resolve ip requests to the name server configured in the host. In this case, the Debian guest doesn't resolve any domain names. How can I configure whatever process is writing /etc/resolv.conf so that it's only written by the dhcp information received over the bridged network (eth0)?