We introduce a hybrid method to determine the neutrino mass hierarchy by simultaneous measurements of responses of at least two detectors to antineutrino and neutrino fluxes from accretion and cooling phases of core-collapse supernovae. The (anti)neutrino-nucleus cross sections for $^{56}$Fe and $^{208}$Pb are calculated in the framework of the relativistic nuclear energy density functional and weak interaction Hamiltonian, while the cross sections for inelastic scattering on free protons $mathrm{p}(bar{ u}_mathrm{e},mathrm{e}^{+})mathrm{n}$ are obtained using heavy-baryon chiral perturbation theory. The modelling of (anti)neutrino fluxes emitted from a protoneutron star in a core-collapse supernova include collective and Mikheyev-Smirnov-Wolfenstein effects inside the exploding star. The particle emission rates from the elementary decay modes of the daughter nuclei are calculated for normal and inverted neutrino mass hierarchy. It is shown that simultaneous use of (anti)neutrino detectors with different target material allows to determine the neutrino mass hierarchy from the ratios of $ u_mathrm{e}$- and $bar{ u}_mathrm{e}$-induced particle emissions. This hybrid method favors neutrinos from the supernova cooling phase and the implementation of detectors with heavier target nuclei ($^{208}$Pb) for the neutrino sector, while for antineutrinos the use of free protons in mineral oil or water is the appropriate choice.
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