Energy band alignments at heterointerfaces play a crucial role in defining the functionality of semiconductor devices, yet the search for material combinations with suitable band alignments remains a challenge for numerous applications. In this work, we demonstrate how changes in deposition conditions can dramatically influence the functional properties of an interface, even within the same material system. The energy band alignment at the heterointerface between Cu2O and ZnO was studied using photoelectron spectroscopy with stepwise deposition of ZnO onto Cu2O and vice versa. A large variation of energy band alignment depending on the deposition conditions of the substrate and the film is observed, with valence band offsets in the range Delta E-VB = 1.45-2.7 eV. The variation of band alignment is accompanied by the occurrence or absence of band bending in either material. It can therefore be ascribed to a pinning of the Fermi level in ZnO and Cu2O, which can be traced back to oxygen vacancies in ZnO and to metallic precipitates in Cu2O. The intrinsic valence band offset for the interface, which is not modified by Fermi level pinning, is derived as Delta E-VB approximate to 1.5 eV, being favorable for solar cell applications.