Transition metal oxides exhibit a high potential for application in the field of electronic devices, energy storage, and energy conversion. The ability of building these types of materials by atomic layer-by-layer techniques provides a possibility to design novel systems with favored functionalities. In this study, by means of the atomic layer-by-layer oxide molecular beam epitaxy technique, we designed oxide heterostructures consisting of tetragonal KNiF-type insulating LaCuO (LCO) and perovskite-type conductive metallic LaNiO (LNO) layers with different thicknesses to assess the heterostructure-thermoelectric property-relationship at high temperatures. We observed that the transport properties depend on the constituent layer thickness, interface intermixing, and oxygen-exchange dynamics in the LCO layers, which occurs at high temperatures. As the thickness of the individual layers was reduced, the electrical conductivity decreased and the sign of the Seebeck coefficient changed, revealing the contribution of the individual layers where possible interfacial contributions cannot be ruled out. High-resolution scanning transmission electron microscopy investigations showed that a substitutional solid solution of La(CuNi)O was formed when the thickness of the constituent layers was decreased.