Efficient interfacial carrier generation in van der Waals heterostructures is critical for their electronic and optoelectronic applications. We demonstrate broadband photocarrier generation in WS2-graphene heterostructures by imaging interlayer coupling-dependent charge generation using ultrafast transient absorption microscopy. Interlayer charge-transfer (CT) transitions and hot carrier injection from graphene allow carrier generation by excitation as low as 0.8 eV below the WS2 bandgap. The experimentally determined interlayer CT transition energies are consistent with those predicted from the first-principles band structure calculation. CT interactions also lead to additional carrier generation in the visible spectral range in the heterostructures compared to that in the single-layer WS2 alone. The lifetime of the charge-separated states is measured to be ~1 ps. These results suggest that interlayer interactions make graphene-two-dimensional semiconductor heterostructures very attractive for photovoltaic and photodetector applications because of the combined benefits of high carrier mobility and enhanced broadband photocarrier generation.