The linearized theory for the parallel propagation of magnetoacoustic-gravity surface waves is developed and a dispersion relation obtained for the case of an isothermal interface of a uniform horizontal magnetic field residing above a field-free medium. The transcendental dispersion relation is solved numerically for a range of parameters and the resulting dispersion curves and corresponding eigenfunctions plotted. As in the case of a uniform Alfv6n speed (Paper I), the existence of the fast and slow magnetoaeoustie-gravity surface modes and the f-mode (modified by the presence of the uniform magnetic field) is determined by the relative temperatures of the two media either side of the interface. If the lower field-free region is cooler than the upper magnetic atmosphere only the slow magnetoacoustic-gravity surface mode may propagate. In addition to these three surface modes we find higher harmonic-type trapped modes. The existence of these modes also depends on the temperatures either side of the interface. They propagate only when both the field-free region is warmer than the magnetic field region and the Alfv6n speed is greater than the corresponding sound speed in the magnetic atmosphere.