The polar Kerr spectra between 0.7 and 4.0 eV of single-crystalline layers of Fe3O4 grown epitaxially on MgAl2O4, SrTiO3 and MgO (100) substrates by means of oxidic molecular beam epitaxy are compared to the spectrum of a bulk synthetic single crystal of magnetite to asses the stoichiometry of the layers. Model calculations of the magneto-optical spectra of thin layers are used to explain the differences between the spectra of bulk Fe3O4 and thin layers of Fe3O4. The observed differences are attributed to interference effects and oxidation of the surface of the thin layers. The results are compared to magnetisation and Verwey transition data.