Problem:

I have been told by an acquaintance that, when traveling on any Inter State Hwy, even if I have a permit and even if I am traveling through a state that honors it; I can not carry the gun on me while on the road. Is that correct?

It makes no sense to me, but I need to be sure.

Solution:

Each state has its own laws on transporting firearms in their state. A good book to have when traveling is:
The Traveler’s Guide to the Firearm Laws of the Fifty States