We have measured the transmission Fourier transform infrared spectra of cubic silicon carbide (3C–SiC polytype) epitaxial layer with a 20 µm thickness on a 200 µm thick silicon substrate. Spectra were recorded in the 400–4000 cm−1 wavenumber range. A novel approach of IR spectra computations based on the recursion capability of the C programming language is presented on the basis of polarized light propagation in layered media using generalized Fresnel's equations. The complex refractive indices are the only input parameters. A remarkable agreement is found between all of the experimental SiC and Si spectral features and the calculated spectra. A comprehensive assignment of (i) the two fundamental transverse optical (TO) (790 cm−1) and longitudinal optical (LO) (970 cm−1) phonon modes of 3C–SiC, (ii) with their overtones (1522–1627 cm−1) and (iii) the two-phonon optical-acoustical summation bands (1311–1409 cm−1) is achieved on the basis of available literature data. This approach allows sorting out the respective contributions of the Si substrate and SiC upper layer. Such calculations can be applied to any medium, provided that the complex refractive index data are known.