[Q] Unusual DNS configuration. Help needed.

[David May]

We currently have a fairly simple DNS configuration for our company
private network + Internet.

Now I have just installed a dial-up connection to a customer's private
network.  Access is permitted through a firewall to selected hosts
such as private Web servers, etc, but no access to their internal DNS.
They have a public DNS server for resolving their public hosts such as
Internet mail server, etc.

I want to configure our DNS to be able to resolve the set of hosts we
are allowed to access on their internal network.  But I still want to
be able use their public DNS server for everything else, such as email.

In case it is unclear why this is a problem consider this:
If I connect via the dialup line to the customer's internal Web 
server with a browser and click on a hyperlink. The browser may 
not be able to resolve the URL as it contains a reference to a 
private hostname on their internal network which not exported by
their public DNS.

I have tried modifying named.conf but failed. My DNS either
resolves only the internal names (itself) or only the public 
names (by referring to the customers public DNS).

Any helpful comments would be appreciated.