In-line rotatable rhombs that are only weakly chromatic are desired as compensators for a wide variety of applications in spectroscopic polarimetry and Mueller matrix spectroscopic ellipsometry. These devices employ multiple total internal reflections to generate differences in the phase shifts upon reflection for orthogonal fast and slow axis optical electric field components. A framework has been developed for characterization of non-idealities in the performance of rhombs due to dissipation and associated dichroism upon each reflection as well as stress-induced birefringence along each beam path. External oblique reflection measurements by spectroscopic ellipsometry for the internally reflecting interface structures has enabled characterization of the dichroic effects and retardance generated by the reflections. The framework for analysis of the effects of stress relies on simulations demonstrating that the contributions to polarization modification from each beam path depend only on the accumulated stress-induced retardance and average azimuthal angle of the fast principal stress axis along the given path. The overall approach has been applied to straight-through Mueller matrix measurements of a three-reflection rhomb in its operational configuration to establish the set of stress parameters for each of the four beam paths needed to fit the measurements. Thus, device geometry and optical structure, including layer thicknesses and component media optical properties, as well as stress-induced retardances and average stress azimuthal angles, which are all deduced in the analysis, enable a complete description of the polarization modifying properties of the rhomb when serving as a compensator.