This letter considers the problem of detecting and characterizing a target buried beneath a rough surface separating two homogeneous half spaces. The problem of detecting the target is tackled by analyzing the frequency-averaged Wigner-Ville function, the purpose of which is to filter out rough surface scattering. Characterization of the target is performed using the iterative solution derived from the Newton-Kantorovitch algorithm as applied to the Wigner-Ville function instead of the scattered field as is usually done. In addition, the scattering model involved in the inversion scheme assumes a flat interface, and surface roughness is handled as clutter. The efficiency of the approach is illustrated through numerical experiments, and the comparison between inversions from the scattered field and the Wigner-Ville function is reported.