Using the complete expansions of the fields and imposing the exact boundary conditions at the interfaces of an irregular stratified medium, Maxwell's equations are transformed into a rigorous set of coupled first-order differential equations for the wave amplitudes. This full wave approach is applied to a large class of propagation problems. Since these solutions account for specular point as well as diffuse scattering in a unified self-consistent manner, it is not necessary to apply a hybrid physical optics-perturbation approach to problems of rough surface scattering. The full wave solutions satisfy realizability, duality and reciprocity relationships in electromagnetic theory. They are invariant to coordinate transformations.