Getting internet from another domain…

Hi. A private Win2k domain is getting internet from a completely separate domain. How would I configure the IIS box if it’s within the private domain and routed to their domain from private firewall to their router. It has to use host.theirdomain.com. I’m thinking proxy or nat but they say “…no it will be under our DNS domain or IT domain but not NT domain” Huh? What am I missing here?