Two-dimensional-on-three-dimensional (2D/3D) halide perovskite heterostructures have been extensively utilized in optoelectronic devices. However, the labile nature of halide perovskites makes it difficult to form such heterostructures with well-defined compositions, orientations, and interfaces, which inhibits understanding of the carrier transfer properties across these heterostructures. Here, we report solution growth of both horizontally and vertically aligned 2D perovskite (PEA)2PbBr4 (PEA = phenylethylammonium) microplates onto 3D CsPbBr3 single crystal thin films, with well-defined heterojunctions. Time-resolved photoluminescence (TRPL) transients of the heterostructures exhibit the monomolecular and bimolecular dynamics expected from exciton annihilation, dissociation, and recombination, as well as evidence for carrier transfer in these heterostructures. Two kinetic models based on Type-I and Type-II band alignments at the interface of horizontal 2D/3D heterostructures are applied to reveal a shift in balance between carrier transfer and recombination: Type-I band alignment better describes the behaviors of heterostructures with thin 2D perovskite microplates but Type-II band alignment better describes those with thick 2D microplates (>150 nm). TRPL of vertically aligned 2D microplates is dominated by directly excited PL and is independent of the height above the 3D film. Electrical measurements reveal current rectification behaviors in both heterostructures with vertical heterostructures showing better electrical transport. As the first systematic study on comparing models of 2D/3D perovskite heterostructures with controlled orientations and compositions, this work provides insights on the charge transfer mechanisms in these perovskite heterostructures and guidelines for designing better optoelectronic devices.