When you start talking legalese, be careful how you use the word "highway", as it's legally basically any road open to the public for transportation--even dirt roads. As such, the public has a right to use them, even in non-motorized fashion (think Amish buggies).

States can limit access to certain high-speed expressways, of course. In California, freeways and interstates are off-limits to bicycles, even in rural areas and deserts, unless there's no reasonable nearby adjacent surface highway. In far southern California, you will be forced off the smooth shoulder of I-8 in the desert onto the nearby, unmaintained Evan Hewes Highway, which seems to have been bombed sometime in the past and never repaired [/sarcasm]