A new model for the scattering of light from layered dielectrics with rough surface boundaries is introduced. The model contains a surface scattering component together with a subsurface scattering component. The former component corresponds to the roughness on the upper surface boundary and is modeled using the modified Beckmann model. The latter component accounts for both refraction due to Fresnel transmission through the layer and rough scattering at the lower layer boundary. By allowing independent roughness parameters for each surface boundary we can achieve excellent fits of the model to the measured BRDF data. Using a well known method of testing reflectance models, we experiment with BRDF data from skin surface samples (human volunteers) and show that the new model outperforms alternative variants of the Beckmann model and the Lafortune et al. reflectance model. As an application in computer graphics, we also show that realistic images of 3D surfaces can be generated using the new model, by setting the values of its physical parameters.