The hybrid measurement system includes an evanescent prism coupling spectroscopy (EPCS) sub-system and a light-scattering polarimetry (LSP) sub-system. The EPCS sub-system includes an EPCS light source optically coupled to an EPCS detector system through an EPCS coupling prism. The LSP sub-system includes an LSP light source optically coupled to an optical compensator, which in turn is optically coupled to a LSP detector system via a LSP coupling prism. A support structure supports the EPCS and LSP coupling prisms to define a coupling prism assembly, which supports the two prisms at a measurement location. Stress measurements made using the EPCS and LSP sub-systems are combined to fully characterize the stress properties of a transparent chemically strengthened substrate. Methods of processing the EPCS and LSP measurements to improve measurement accuracy are also disclosed.