The perdiction of the Resonance Scattering Theory (RST) for the reflection coefficient from a set of two contiguous plane dielectric layers separating two semi-infinite dissimilar non-conducting media, is constructed and compared to the exact classical model solution. The comparsion serves to: a) show the accuracy and simplicity of the RST prediction, and b) to underline the usefulness of the RST to produce simple physical interpretations of generally complex phenomena. The analysis provides a systematic method for detecting the presence of a dielectric layer under another one covering it (possibly the situation caused by an oil spill in ice-covered Artic regions), by certain modulation effects present in the 'response surface' of the returned echoes. This method also identifies the material composition of the lower or hidden layer in the bilaminar configuration. The process disentangles which resonance feature present in the radar reflection coefficient is caused by which of the two interacting layers. RST, therfore, solves the inverse scattering problem for the composition and thickness not only of the top visible (ice) layer, but also of the substance (oil) hidden under that upper layer.