The time-dependent Mueller matrix solution of vector radiative transfer for inhomogeneous random media of non-spherical scatterers is presented. Co-polarized and cross-polarized bistatic scatterings for a polarized pulse incidence are numerically simulated. Numerical results well demonstrate volumetric and surface scattering mechanism and depict the inhomogeneous fraction profile of random scatterers. The peak tails in polarized echoes due to wave reflections from the underlying surface can be identified. Its co-polarized peaks in the specular direction are applied to simultaneous retrievals of the underlying surface roughness and moisture in the presence of inhomogeneous vegetation canopy.