Perovskite nanocrystals (NCs) are an emergent and game-changing entrant in semiconductor research, yet the research on the corresponding nanoheterostructures remains in its infancy. In this work, we fabricate a type II nanoarchitecture of CsPbX3 NCs (where X = Cl, Br, or I) and CuInS2 quantum dots to investigate the energy and charge transfer (ET and CT, respectively) processes. Optical measurements of CsPbX3/CuInS2 show efficient photoluminescence (PL) quenching when X = Br or I, while the PL quenching efficiency of the X = Cl compound is 2 orders of magnitude lower. We argue the drastic PL quenching in the X = I compound is solely due to the CT process, while for the X = Br compound, a predominantly ET process is active. In contrast to the driving force (-ΔG) for the CT process, we observe the reverse order of the electron transfer process, for which we propose the electron transfer occurs in the Marcus inverted region. Our halide-dependent controlled regulation of CT and ET processes in these nanoarchitectures may find promising optoelectronic applications.