Electrical techniques based on capacitance and conductance measurements are powerful tools for interface characterization in semiconductor heterostructures. We here detail their application to the study of the heterointerface formed between hydrogenated amorphous silicon (a-Si:H) and crystalline silicon (c-Si). The main parameters governing the device applications are the conduction and valence band mismatch, and the density of interface states. The presence of a high interface states density can be revealed by capacitance versus temperature and frequency measurements. For very high quality interfaces that are required for instance to reach high conversion efficiencies in solar cells, the usual measurements performed in the dark and at zero or reverse bias are not sensitive enough. We show that the sensivity to interface states can be enhanced by using capacitance measurements under illumination and at a forward bias close or equal to the open-circuit voltage. In this case, the measured capacitance is determined by the diffusion of free carriers in c-Si and limited by recombination at the interface. Regarding the determination of band offsets, the method using a plot of the inverse square capacitance as a function of bias to determine the intercept of the extrapolated linear region is shown to lead to errors even in the absence of any interface charge. This is due to the presence of a strong inversion layer in c-Si at the interface, the effect of which has been ignored so far in the literature. The presence of this strong inversion layer is evidenced from planar conductance measurements on (n) a-Si:H/(p) c-Si structures. We emphasize that these measurements are very sensitive to details of the band structure profile. In particular, it is shown that the temperature dependence of the sheet electron density allows the determination of the conduction band offset between a-Si:H and c-Si with a good precision. We find 0.15 ± 0.04 eV.