Epitaxial thin-film heterostructures of the strongly spin-orbit coupled Mott-insulator Sr2IrO4 (SIO) and the cuprate high temperature superconductor YBa2Cu3O7 − δ (YBCO) are grown with pulsed laser deposition (PLD). A high crystalline quality is confirmed with X ray diffraction. The magnetic order of single SIO layers is studied with dc magnetization and low-energy muon spin rotation measurements and resembles that of the bulk material with a canted antiferromagnetic order. The electronic normal state and superconducting properties of YBCO (10, 12, or 14 nm)–SIO (20 nm) and inversely stacked SIO (20nm)–YBCO (10, 12, or 14 nm) bilayers are studied with dc resistivity measurements and found to be strongly dependent on the sequence of the layer stacking. The YBCO–SIO bilayers with d(YBCO) = 14nm, 12 nm, and 10 nm are all metallic and superconducting with an onset temperature around 85K and zero resistivity below 65K. To the contrary, for the inversely stacked SIO–YBCO bilayers a metallic and superconducting response occurs only at d(YBCO) = 14 nm, whereas