The quantum de Haas-van Alphen (dHvA) and Shubnikov-de Haas oscillations measured in graphite were decomposed by pass-band filtering onto contributions from three different groups of carriers. Generalizing the theory of dHvA oscillations for 2D carriers with an arbitrary spectrum and by detecting the oscillation frequencies using a method of two-dimensional phase-frequency analysis which we developed, we identified these carriers as (i) minority holes having a 2D parabolic massive spectrum p(2)(perpendicular)/2m(perpendicular), (ii) massive majority electrons with a 3D spectrum and (iii) majority holes with a 2D Dirac-like spectrum +/-vp(perpendicular) which seems to be responsible for the unusual strongly-correlated electronic phenomena in graphite.