Aims. We derive the spectra of the cosmic X-ray background (CXB) and of the Galactic ridge X-ray emission (GRXE) in the 20-200 keV range from the data of the IBIS instrument aboard the INTEGRAL satellite obtained during the four dedicated Earth-occultation observations in early 2006.

Methods. We analyze the modulation of the IBIS/ISGRI detector counts induced by the passage of the Earth through the field of view of the instrument. Unlike previous studies, we do not fix the spectral shape of the various contributions, but model instead their spatial distribution and derive for each of them the expected modulation of the detector counts. The spectra of the diffuse emission components are obtained by fitting the normalizations of the model lightcurves to the observed modulation in different energy bins. Because of degeneracy, we guide the fits with a realistic choice of the input parameters and a constraint for spectral smoothness.

Results. The obtained CXB spectrum is consistent with the historic HEAO-1 results and falls slightly below the spectrum derived with Swift/BAT. A 10% higher normalization of the CXB cannot be completely excluded, but it would imply an unrealistically high albedo of the Earth. The derived spectrum of the GRXE confirms the presence of a minimum around 80 keV with improved statistics and yields an estimate of 0.6 for the average mass of white dwarfs in the Galaxy. The analysis also provides updated normalizations for the spectra of the Earth's albedo and the cosmic-ray induced atmospheric emission.

Conclusions. This study demonstrates the potential of INTEGRAL Earth-occultation observations to derive the hard X-ray spectra of three fundamental components: the CXB, the GRXE and the Earth emission. Further observations would be extremely valuable to confirm our results with improved statistics.