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Single-crystal layered perovskite heterostructures provide a scalable platform for potentially realizing emergent properties recently seen in mechanically stacked monolayers. We report two new layered perovskite heterostructures M2(PbCl2)(AMCHC)2(PbCl4)·2H2O (1_M where M = Na+, Li+; AMCHC = +NH3CH2C6H10COO‒) crystallizing in the chiral, polar space group C2. The heterostructures exhibit alternating layers of a lead-chloride perovskite and an intergrowth comprising corner-sharing PbCl4(η2-COO)2 polyhedra with bridging equatorial chlorides and terminal axial oxygen ligands. Small alkali metal cations and water molecules occupy the cavities between the polyhedra in the intergrowth layer. The heterostructures display wide bandgaps and two closely spaced excitonic features in their optical spectra and strong second harmonic generation. The calculated band structure of 1_Na features a Type-I quantum-well structure, where the electron-hole correlation function corresponding to the lowest excited state points to electron-hole pairs localized within a single inorganic layer (intralayer excitons), as seen in typical layered halide perovskites. In contrast, calculations show that 1_Li adopts a Type II quantum-well structure, with electrons and holes in the lowest-excited state residing in different inorganic layers (interlayer excitons). Calculations on model complexes suggest that these changes in band alignment, between Type-I and Type-II quantum-well structures, are driven by the placement of the alkali metal and the orientation of the water molecules changing the electrostatic potential-energy profiles of the heterostructures. Thus, this study sets the stage for accessing different alignments of the perovskite and intergrowth bands in bulk perovskite heterostructures that self-assemble in solution.