The mobilities of electrons and holes determine the applicability of any semiconductor, but their individual measurement remains a major challenge. Here, we show that time-resolved terahertz spectroscopy (TRTS) can distinguish the mobilities of minority and majority charge carriers independently of the doping-type and without electrical contacts. To this end, we combine the well-established determination of the sum of electron and hole mobilities from photo-induced THz absorption spectra with mobility-dependent ambipolar modeling of TRTS transients. The method is demonstrated on a polycrystalline Cu2ZnSnSe4 thin film and reveals a minority (electron) mobility of 128 cm2/V-s and a majority (hole) carrier mobility of 7 cm2/V-s in the vertical transport direction relevant for light emitting, photovoltaic and solar water splitting devices. Additionally, the TRTS analysis yields an effective bulk carrier lifetime of 4.4 ns, a surface recombination velocity of 6 * 104 cm/s and a doping concentration of ca. 1016 cm-3, thus offering the potential for contactless screen novel optoelectronic materials.