The first self-consistent transport-theoretic model for the combined electron-proton-hydrogen atom aurora is presented. This is needed for accurate modeling of the diffuse aurora, particularly in the midnight sector, for which a statistical study (Hardy et al., 1989) indicates that the proton contribution to the total auroral energy flux is (on the average) about 20 to 25% of that of the electrons. As a result, the ionization yield as well as the yields of many emission features will be underestimated (on the average) by about the same percentage if the proton-hydrogen atom contributions are neglected. The model presented here can also be used to study a pure electron aurora or a pure proton-hydrogen atom aurora by choosing the appropriate boundary conditions, namely, by setting the incident flux of one or the other particle population equal to zero. In the latter case, the new feature of the present model is the rigorous transport-theoretic treatment of the contributions to ionization rates and to emission rates and yields from the secondary electrons produced by protons and hydrogen atoms. A coupled set of three linear transport equations is presented. Protons and hydrogen atoms are coupled only to each other through charge-changing (charge exchange and stripping) collisions, while the electrons are coupled to both protons and hydrogen atoms through the secondary electrons that they produce. Source functions for the secondary electrons produced by the three primary particle populations are compared and contrasted, and the numerical methods for solving the coupled transport equations are described. Finally, formulas for calculating pertinent aurora-related quantities from the particle fluxes are given. In the companion paper (Strickland et al., this issue), the model results are presented. ¿ American Geophysical Union 1993