Conductive-probe atomic force microscopy (CP-AFM) measurements reveal the existence of a conductive channel at the interface between p-type hydrogenated amorphous silicon (a-Si:H) and n-type crystalline silicon (c-Si) as well as at the interface between n-type a-Si:H and p-type c-Si. This is in good agreement with planar conductance measurements that show a large interface conductance. It is demonstrated that these features are related to the existence of a strong inversion layer of holes at the c-Si surface of (p) a-Si:H/(n) c-Si structures, and to a strong inversion layer of electrons at the c-Si surface of (n) a-Si:H/(p) c-Si heterojunctions. These are intimately related to the band offsets, which allows us to determine these parameters with good precision.