Magnetoresistivity ρ(xx) and Hall resistivity ρ(xy) in ultrahigh magnetic fields up to 88 T are measured down to 0.15 K to clarify the multiband electronic structure in high-quality single crystals of superconducting FeSe. At low temperatures and high fields we observe quantum oscillations in both resistivity and the Hall effect, confirming the multiband Fermi surface with small volumes. We propose a novel approach to identify from magnetotransport measurements the sign of the charge carriers corresponding to a particular cyclotron orbit in a compensated metal. The observed significant differences in the relative amplitudes of the quantum oscillations between the ρ(xx) and ρ(xy) components, together with the positive sign of the high-field ρ(xy), reveal that the largest pocket should correspond to the hole band. The low-field magnetotransport data in the normal state suggest that, in addition to one hole and one almost compensated electron band, the orthorhombic phase of FeSe exhibits an additional tiny electron pocket with a high mobility.