A numerical model is applied in a Monte Carlo study of scattering from a three-dimensional penetrable object above a lossy dielectric rough interface. The model is based on an iterative method of moments solution for equivalent electric and magnetic surface current densities on the rough interface and equivalent volumetric electric currents in the penetrable object. Both time-and frequency-domain results are investigated to illustrate the relative importance of coherent and incoherent scattering effects in the sample problem considered. Results show that a four-path model using a reduced-reflection coefficient can be reasonable for coherent scattering predictions and that incoherent object/surface interaction effects can make significant contributions to received cross sections.