We demonstrate that a dual-layer, dual-color scintillator construct for microscopic CT, originally proposed to increase sensitivity in synchrotron imaging, can also be used to perform material quantification and classification when coupled with polychromatic illumination. We consider two different approaches to data handling: (1) a data-domain material decomposition whose estimation performance can be characterized by the Cramer-Rao lower bound formalism but which requires careful calibration and (2) an image-domain material classification approach that is more robust to calibration errors. The data-domain analysis indicates that useful levels of SNR (>5) could be achieved in one second or less at typical bending magnet fluxes for relatively large amounts of contrast (several mm path length, such as in a fluid flow experiment) and at typical undulator fluxes for small amount of contrast (tens of microns path length, such as an angiography experiment). The tools introduced could of course be used to study and optimize parameters for a wider range of potential applications. The image domain approach was analyzed in terms of its ability to distinguish different elemental stains by characterizing the angle between the lines traced out in a two-dimensional space of effective attenuation coefficient in the front and back layer images. This approach was implemented at a synchrotron and the results were consistent with simulation predictions.