Hi,
My answer is along the same lines of the answer provided by jodylemoine.
Assuming you can use an external DNS Server to resolve your Squid queries and an Internal DNS server to resolve the queries from the Server, you can -
a) Add reference to the the Local DNS Server Ip Address in your Server
b) Add reference to the External DNS server Ip Address in your Squid Configuration file. Add the following parameter to your squid.conf file and reload squid
dns_nameservers <Ip Address of External DNS Server>