Cu2O/ZnO has been envisaged as a potential material system for the next generation thin film solar cells. So far, the experimental efforts to obtain conversion efficiencies close to the theoretically predicted value have failed. Combining aberration-corrected (scanning) transmission electron microscopy and density functional theory modelling, we have studied the interfaces between single crystal c-axis oriented ZnO and high-quality magnetron sputtered Cu2O films. Strikingly, our study shows that the first ~5 nm of the Cu-oxide films have the structure of the monoclinic CuO phase. The CuO layer is textured with the (111), (11¯1), (¯111), (1¯1 ¯1), (¯1 ¯11), (1¯11), (¯11¯1) and (100) planes parallel to the (0001) and (000¯1) ZnO interfaces. The ionic arrangement on these planes resembles the hexagonal arrangement of the ZnO interface and epitaxy exists across the interface. A continued epitaxial growth of  oriented Cu2O follows resulting in epitaxial 180o rotation twins in the Cu2O layer. For the case with the (100)CuO interfacial plane we have: (111)[1¯10]Cu2O II (100)CuO II (0001)[11¯20]ZnO. Because of a closer lattice matching of CuO with ZnO and Cu2O, the total strain and energy is reduced compared to a pure (111)Cu2O II (0001)ZnO interface. The existence of CuO is anticipated to be a contributing factor for the low conversion efficiencies obtained experimentally.