This paper addresses the problem of classifying materials from microspectroscopy at a pixel level. The challenges lie in identifying discriminatory spectral features and obtaining accurate and interpretable models relating spectra and class labels. We approach the problem by designing a supervised classifier from a tandem of Artificial Neural Network (ANN) models that identify relevant features in raw spectra and achieve high classification accuracy. The tandem of ANN models is meshed with classification rule extraction methods to lower the model complexity and to achieve interpretability of the resulting model. The contribution of the work is in designing each ANN model based on the microspectroscopy hypothesis about a discriminatory feature of a certain target class being composed of a linear combination of spectra. The novelty lies in meshing ANN and decision rule models into a tandem configuration to achieve accurate and interpretable classification results. The proposed method was evaluated using a set of broadband coherent anti-Stokes Raman scattering (BCARS) microscopy cell images (600 000 pixel-level spectra) and a reference four-class rule-based model previously created by biochemical experts. The generated classification rule-based model was on average 85% accurate measured by the DICE pixel label similarity metric, and on average 96% similar to the reference rules measured by the vector cosine metric.