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[Display omitted] Two-dimensional (2D) van der Waals (vdW) heterostructures offer new platforms for exploring novel physics and diverse applications ranging from electronics and photonics to optoelectronics at the nanoscale. The studies to date have largely focused on transition-metal dichalcogenides (TMDCs) based samples prepared by mechanical exfoliation method, therefore it is of significant interests to study high-quality vdW heterostructures using novel materials prepared by a versatile method. Here, we report a two-step vapor phase growth process for the creation of high-quality vdW heterostructures based on perovskites and TMDCs, such as 2D Cs 3 Bi 2 I 9 /MoSe 2 , with a large lattice mismatch. Supported by experimental and theoretical investigations, we discover that the Cs 3 Bi 2 I 9 /MoSe 2 vdW heterostructure possesses hybrid band alignments consisting of type-I and type-II heterojunctions because of the existence of defect energy levels in Cs 3 Bi 2 I 9. More importantly, we demonstrate that the type-II heterojunction in the Cs 3 Bi 2 I 9 /MoSe 2 vdW heterostructure not only shows a higher interlayer exciton density, but also exhibits a longer interlayer exciton lifetime than traditional 2D TMDCs based type-II heterostructures. We attribute this phenomenon to the reduced overlap of electron and hole wavefunctions caused by the large lattice mismatch. Our work demonstrates that it is possible to directly grow high-quality vdW heterostructures based on entirely different materials which provide promising platforms for exploring novel physics and cutting-edge applications, such as optoelectronics, valleytronics, and high-temperature superfluidity. [ABSTRACT FROM AUTHOR]