Earth medium effects in the three-neutrino oscillations of atmospheric neutrinos are observable under appropriate conditions. This paper generalizes the study of the medium effects and the possibility of their observation in the atmospheric neutrino oscillations from the case of neutrinos traversing only the Earth mantle, where the density is essentially constant, to the case of atmospheric neutrinos crossing also the Earth core. In the latter case new resonance-like effects become apparent. We calculate the CPT-odd asymmetry for the survival probability of muon neutrinos and the observable muon-charge asymmetry, taking into account the different atmospheric neutrino fluxes, and show the dependence of these asymmetries on the sign of Δm231 and on the magnitude of the mixing angle θ13. A magnetized detector with a sufficiently good neutrino momentum resolution is required for the observation of the muon-charge asymmetry generated by the Earth mantle-core effect.