This paper assesses the interface stability of the perovskite CsPbBr3 and transport layer CuI using density functional theory and band offset calculations. As a low-cost, more stable alternative to current hole transport materials, CuI may be used to template the epitaxial growth of perovskites such as CsPbBr3 owing to a 1% lattice constant mismatch and larger bulk modulus. We compare all eight atomic terminations of the interfaces between the (100) low-energy facet for both CsPbBr3 and CuI, increasing material thickness to consider charge density redistribution and bonding characteristics between surface and bulk-like regions. A low energy atomic termination is found to exist between these materials where alternating charge accumulation and depletion regions stabilize bonds at the interface. Band offset calculations reveal a type I straddling gap offset in the bulk shifting to a type II staggered gap offset as the thickness of the materials is increased, where the built-in potential changes as layer thickness increases, indicating the tunability of charge separation at the interface. CuI may, thus, be used as an alternative hole transport layer material in CsPbBr3 optoelectronic devices.