We investigate the structural and electronic properties of the interface between hydrogenated amorphous silicon (a-Si:H) and crystalline silicon (c-Si) by combining tight-binding molecular dynamics and DFT ab initio electronic structure calculations. We focus on the c-Si(100)(1×1)/a-Si:H, c-Si(100)(2×1)/a-Si:H and c-Si(111)/a-Si:H interfaces, due to their technological relevance. The analysis of atomic rearrangements induced at the interface by the interaction between H and Si allowed us to identify the relevant steps that lead to the transformation from c-Si(100)(1×1)/a-Si:H to c-Si(100)(2×1)/a-Si:H. The interface electronic structure is found to be characterized by spatially localized mid-gap states. Through them we have identified the relevant atomic structures responsible for the interface defect states, namely: dangling-bonds, H bridges, and strained bonds. Our analysis contributes to a better understanding of the role of such defects in c-Si/a-Si:H interfaces.