The concentration and temperature dependences of the electrical and thermal conductivity of epoxy-based (L285) composite materials (СM) with a combined graphite nanoplatelets/carbonyl iron (GNP/Fe) filler are studied. The content of GNP is varied from 0.7 to 4.0% vol., and the content of Fe was 5.6% vol. As found, the addition of Fe particles in the GNP/L285 composite leads to a decrease in thermal conductivity and a more complex dependence of thermal conductivity on the concentration of GNP. Such changes in thermal conductivity for three-phase CM can be related to an increase in thermal contact resistance at the interfacial boundaries of the matrix–filler, the number of which increases significantly with the addition of Fe particles. Experimental concentration dependences of thermal conductivity of two- and three-phase CM with GNP filler are described in the framework of the combined model of mixtures. The features of the temperature dependences of the thermal conductivity of two-phase CM GNP/L285, Fe/L285 and three-phase composites GNP/Fe/L285 are determined by increasing the concentration of phonons and increasing phonon–phonon scattering when heated. As found, the addition of 5.6% vol. of dispersed Fe particles in a two-phase GNP/L285 composite has almost no effect on the percolation threshold, the value of which is $\phi_{\textrm{c}}$ = 1.8% vol. This means that electrically conductive chains are formed mainly from GNP particles in the hybrid composite, and electrically conductive particles do not form individual continuous chains and can only act as ‘bridges’ connecting GNP particles in electrically conductive chains. For concentrations of hybrid filler above the percolation threshold, the number of electrically conductive chains and the value of contact electrical resistance between GNP particles are estimated within the framework of model of the effective electrical resistance. It is shown that in CM with GNP content which is less and near the percolation threshold electronic transport in composites is carried out mainly due to the hopping mechanism of conductivity, and at GNP concentrations above the percolation threshold the tunnelling mechanism of conductivity is realized due to the formation of a large number of electrically conductive chains with a small gap between the conductive particles.