A spectroscopy system developed to measure directional and spectral characteristics of semi-transparent media encountered in solar thermal and thermochemical applications is presented. The system incorporates a double monochromator coupled to a double radiation source and a rotary multi-element sandwich detector to enable measurements in the spectral range between 0.3-4 mu m. Direct iterative and inverse radiative transfer techniques are employed to extract radiative properties of interest from bi-directional reflectance and transmittance measurements. Two examples demonstrating the feasibility of the method are given: (1) the determination of the extinction coefficient of reticulate porous ceramics and (2) the extraction of a complete set of radiative properties for a packed bed of particles.