  We present a robust, precise, and accurate method to simultaneously measure
the refractive indices of two transparent materials within an interference
coating. This is achieved by measuring both a photometrically accurate
transmittance spectrum and the as-grown individual layer thicknesses of a
thin-film multilayer structure. These measurements are used for a TMM-based
curve-fitting routine which extracts the refractive indices and their
measurement uncertainties via a Monte-Carlo-type error propagation. We
demonstrate the performance of this approach by experimentally measuring the
refractive indices of both, GaAs and Al$_{0.929}$Ga$_{0.071}$As, as present in
an epitaxial distributed Bragg reflector. A variety of devices can be used to
obtain the transmittance spectrum (e.g., FTIR, grating-based spectrophotometer)
and layer thicknesses (e.g., SEM, TEM, AFM), the discussed approach is readily
adaptable to virtually any wavelength region and many transparent material
combinations of interest. The subsequent model-fitting approach yields
refractive index values with $10^{-4}$-level uncertainty for both materials.
