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We have measured the dielectric function of bulk nitrogen-doped 4H and 6H SiC substrates from 700 to 4000 cm-1 using Fourier-transform infrared spectroscopic ellipsometry. Photon absorption by transverse optical phonons produces a strong reststrahlen band between 797 and 1000 cm-1 with the effects of phonon anisotropy being observed in the region of the longitudinal phonon energy (960 to 100 cm-1). The shape of this band is influenced by plasma oscillations of free electrons, which we describe with a classical Drude equation. For the 6H-SiC samples, we modify the Drude equation to account for the strong effective mass anisotropy. Detailed numerical regression analysis yields the free-electron concentrations, which range from 7x1017 to 1019 cm23, in good agreement with electrical and secondary ion mass spectrometry measurements. Finally, we observe the Berreman effect near the longitudinal optical phonon energy in n-/n+ homoepitaxial 4H SiC and hydrogen implanted samples, and we are able to determine the thickness of these surface layers.