A sharp potential drop across the interface of the Pb-rich halide perovskites/TiO2 heterostructure is predicted from first-principles calculations, suggesting enhanced separation of photoinduced charge carriers in the perovskite-based photovoltaic solar cells. The potential drop appears to be associated with the charge accumulation at the polar interface. More importantly, on account of both the beta phase structure of CH3NH3SnxPb1-xI3 for x < 0.5 and the a phase structure of CH3NH3SnxPb1-xI3 for x = 0.5, the computed optical absorption spectra from time-dependent density functional theory (TD-DFT) are in very good agreement with the measured spectra from previous experiments. Our TD-DFT computation also confirms the experimental structures of the mixed Pb-Sn organometal halide perovskites. These computation results provide a highly sought answer to the question why the lead-based halide perovskites possess much higher power conversion efficiencies than the tin-based counterparts for solar-cell applications.