Spectral analysis of the Shubnikov-de Haas magnetoresistance oscillations and the quantum Hall effect (QHE) measured in quasi-2D highly oriented pyrolytic graphite (HOPG) [Phys. Rev. Lett. 90, 156402 (2003)] reveals two types of carriers: normal (massive) electrons with Berry phase 0 and Dirac-like (massless) holes with Berry phase pi. We demonstrate that recently reported integer- and semi-integer QHEs for bilayer and single-layer graphenes take place simultaneously in HOPG samples.