private domain & internet email coexist?

OL2K/2K3;Ex2K/2K3:Can transports for private (internal) domain & internet (POP3/SMTP) coexist? When setting up both on same client,get undeliverable for internet when internal transport set as primary, then private returned when ISP attempts to route mail w/our private domain name. Tried SMTP connectors, either lack of knowledge or not right tool. This should be fairly common cfg… help!