My best take at solving this is having a flag or configuration option somewhere that changes the resolver's "query DNS server only when previous is down" behavior to "query DNS server when first gives a negative answer". And then have the distro's network scripts adding the DNS servers that come from the other interfaces by DHCP added to resolv.conf if the second behavior is selected.
You might want to ask about this on the ISC BIND list (after checking its archives). I'm sure the subject comes up regularly there. Any proposed change to resolver behavior should start there.
