This paper deals with the study of wave propagation and scattering in a half-space random medium with a random interface. The surface randomness and the volume randomness are treated with equal importance and a multiple scattering solution is sought. The random fluctuations of both the random medium and the surface are assumed to be small and obey Gaussian statistics. These assumptions enable us to use approximations and physically identify the various scattering processes. The Feynman diagram technique is used to derive the Dyson equation and the Bethe-Salpeter (B-S) equation for the first and second moments of Green's functions, respectively. Two approximations, viz., the bilocal approximation and the nonlinear approximation are applied to the Dyson equation. Proceeding along similar lines the ladder approximation is applied to the B-S equation. The Feynman diagram technique affords us to clearly identify the scattering interaction between the random surface and the random medium. These interactions which are usually ignored in a single scattering approximation become important in a multiple scattering solution.