Excellent charge carrier behavior in hydrogenated amorphous silicon/crystalline silicon (a-Si:H/c-Si) is crucial for achieving the high efficiency and stability of Si heterojunction solar cells. In this work, we employ the real-time time-dependent density functional based tight binding (TD-DFTB) approach with the Ehrenfest dynamic method to investigate how vibronic coupling affects the photoinduced charge behavior in a-Si:H/c-Si. The variation in hydrogen concentration demonstrates the diversity of intermaterial charge transfer. The hydrogen directly leads to structural differences and thus indirectly affects charge separation and transfer, emphasizing the importance of hydrogen in the charge transfer process. Doping c-Si with aluminum or phosphorus improves the intermaterial charge separation transfer and, to some extent, suppresses charge carrier recombination. Furthermore, lattice vibration mode analysis shows that, while a-Si:H primarily contributes to defect passivation and carrier-selective transporting, the charge separation and transfer are also significantly affected. The intense phonon vibration modes indicate the presence of a nonradiative recombination mechanism, which results in the gradual energy fading.