As single junction thin-film technologies, both Si heterojunction (HIT) and Perovskite based solar cells promise high efficiencies at low cost. One expects that a tandem cell design with these cells connected in series will improve the efficiency further. Using a self-consistent numerical modeling of optical and transport characteristics, however, we find that a traditional series connected tandem design suffers from low due to band-gap mismatch and current matching constraints. It requires careful thickness optimization of Perovskite to achieve any noticeable efficiency gain. Specifically, a traditional tandem cell with state-of-the-art HIT () and Perovskite ( ) sub-cells provides only a modest tandem efficiency of 25%. Instead, we demonstrate that a bifacial HIT/Perovskite tandem design decouples the optoelectronic constraints and provides an innovative path for extraordinary efficiencies. In the bifacial configuration, the same state-of the-art sub-cells achieve a normalized output of =33%, exceeding the bifacial HIT performance at practical albedo reflections. Unlike the traditional design, this bifacial design is relatively insensitive to Perovskite thickness variations, which may translate to simpler manufacture and higher yield.