Confocal scanning combined with low-coherence interferometry is used to provide remote refractive index and thickness measurements of transparent materials. The influence of lens aberrations in the confocal measurement is assessed through ray-trace modeling of the axial point-spread functions generated using optical configurations comprised of paired aspherics and paired achromats. Off-axis parabolic mirrors are suggested as an alternative to lenses and are shown to exhibit much more symmetric profiles provided the system numerical aperture is not too high. The modeled results compare favorably with experimental data generated using an optical instrument comprised of a broadband source and line-scan spectrometer. Refractive index and thickness measurements are made with each configuration with most mirror pairings offering better than twice the repeatability and accuracy of either lens pairing.