DNS Setup

We currently have Exchange 5.5, IIS 4, and MS Proxy on an NT 4 system. My question is what setup should I use for my organization? We have our own in-house website at Coffercorp.com, the DNS for that is handled by our ISP, but we also want to have an Intranet, so what should my config look like. Currently we have an Internal DNS server that has every server and client using XXX.coffercorp.com (where XXX is the host name), should it be XXX.coffercorp.com for the external addressing (web site/Email) and XXX.coffercorp.net for all internal machines, or is my config accurate, we want the best security possible so any help is appreciated?