Magnetic circular dichroism (MCD) spectra taken at the M2,3 absorption edge of thin Fe films exhibit pronounced thickness-dependent variations in the MCD signal and line shape which are related to birefringence effects in the ferromagnetic film. Model calculations based on the Maxwell-Fresnel formalism are used to calculate the different interference effects occurring for left and right circularly polarized light reflected from the vacuum/film/substrate interfaces. The M2,3 MCD experiments confirm the magnitude and thickness dependent periodicity predicted by the macroscopic theory. The data clearly demonstrate the importance of the interference effects which are very pronounced for film thicknesses up to several units of the excitation wavelength. While at the Fe M2,3 transition the thickness corresponding to the wavelength unit is about 220 Å, the same effects are to be expected in the Fe L2,3 spectra for considerably thinner films since the wavelength is only ~17 Å. The observed interference effects are of general character and caution should be employed in attempts to relate changes in the L2,3 MCD spectra of several-monolayer thin films solely to the formation or reorientation of magnetic moments and to their decomposition into spin and orbital components. Because the theory employed here considers the total power dissipated in the reflection/absorption process rather than amplitudes of reflected waves, interference effects are not restricted to reflection MCD measurements but should also be present in a slightly modified form in the more commonly used total electron yield type absorption MCD experiment.