While flying from Osaka to Sydney via Canton on China Southern Airlines, I saw a map entitled "Domestic Flight Routing Map of China Southern Airlines" in the in-flight magazine, which included Taipei, Taichung and Kaohsiung.

Is it possible, either using China Southern or some other airline, to take a "domestic" flight between two countries?

I tried working out whether China Southern itself treats a flight from Canton to Taipei as a domestic flight, but didn't see any information before the stage of the booking process where I would have to put credit card info in.

Criteria:

 1. The airline has separate categories of "domestic" and "international". Ideally, there should be actual differences between the two, such as how early you need to arrive at the airport, or whether you're allowed to bring water on-board.
 2. The travel doesn't involve an illegal border crossing.
 3. Neither country is a micronation - it either has to be a UN recognised country, or listed in Wikipedia's article [List of states with limited recognition][1]
 4. Ideally it should involve a territorial dispute, but special arrangements between two countries (eg the EU, or Australia and New Zealand) may be relevant.

Related question, but about how a government itself perceives travel to a disputed territory: http://travel.stackexchange.com/questions/22690/would-china-to-taiwan-and-back-again-count-as-another-entry-into-china

  [1]: https://en.wikipedia.org/wiki/List_of_states_with_limited_recognition