One company I used to work for used intra.<company>.com as their intranet domain, where the "intra" subdomain only existed internally. Seemed to work quite well.
I do something similar, with machines on the internal LAN being in the subdomain home.mypublic.domain. However, there are a few gotchas when an externally visible server has one (NATted) address to the outside world and an internal RFC 1918 address internally. Nothing that the knowledgeable can't handle provided they understand DNS and have a sensible gateway, but not for the average punter. This is one area where IPv6 will make life simpler, as all internal addresses will be globally routable without NAT. (I really must sort out IPv6 this year.)