You only have to have international segments on the member airlines: Aces, Aeropostal, Avianca, Aviateca, Copa, Lacsa, Nica, Saeta, Taca, and Taca-Perú. Note that Grupo Taca is not one airline, but four: Aviateca, Lacsa, Nica, and Taca. Nica is no longer flying, so a flight from MIA to MGA on Lacsa or Taca will fill the Nica requirement.
LatinPass has not said that the partner airline flights have to be international. Also, while National Airlines is now a partner airline, the official rules on the LatinPass web site only mention TWA, KLM, and USAirways as qualifying for this promotion. So if you're going to fly National, be sure to get something in writing from LatinPass first (and let us all know what they say!).