Starting from an expression for the Gibbs energy derived previously for a monolayer consisting of a single amphiphilic component present in the (LE/LC) coexistence region, the general thermodynamic criteria for internal equilibrium are derived. It is assumed that the solid phase is present as a dispersion of equally sized circular islands. The assumption of isodispersity is justified by the results of an earlier study. The necessary and sufficient conditions for stability of the equilibria are formulated within the constraints imposed by the model. All of these are stated in a general form, independent of the specific analytical expressions for the various thermodynamic quantities. It is pointed out that a more or less complete analysis will only be possible once an explicit expression for the line tension and an equation of state for a 2D fluid of rigid disks with smeared-out dipole moment become available. The latter would allow the calculation of the free energy of mixing, G(mix),, as well as the formulation of a 2D equation of state for the film within the coexistence region of the phase diagram. A generic functional form of these functions is given that is consistent with the requirements set by dimensional analysis. Finally, generalizations of the thermodynamic formalism to mixed monolayers and noncircular domain shapes are suggested.