Pigment identification and mapping gives us insight into an artists' material use, allows us to measure slow chemical changes in painted surfaces, and allows us to detect anachronistic uses of materials that can be associated with either forgeries or past restorations. Earlier work has demonstrated the potential of a dictionary-based reflectance approach for pigment classification. This technique identifies pigments by searching for the pigment combinations that best reproduce the measured reflectance curve. The prospect of pigment classification through modeling is attractive because it can be extended to a layered medium -- potentially opening a route to a depth-resolved pigment classification method. In this work, we investigate a layered pigment classification technique with a fused deep learning and optimization-based Kubelka-Munk framework. First, we discuss the efficacy of the algorithm in a thick, single-layer system. Specifically, we consider the impacts of layer thickness, total pigment concentration, and spectrally similar pigment combinations. Following a thorough discussion of the single layer problem, the system is generalized to multiple layers. Finally, as a concrete example, we use the two-layered system to demonstrate both the impacts of layer thickness and dictionary content on paint localization within the painting. Results of the algorithm are then shown for mock-up paintings for which the ground truth is known.