We have studied YBa2Cu3Oy bi-layer thin films deposited at two different temperatures on mismatched substrates, such as MgO (a=b=c=0.412nm) and YSZ (a=b=c=0.5139nm). The bottom layer is deposited at a lower temperature (660 degrees C) while the top layer is deposited at the usual temperature (750 degrees C). The Tc of the bilayer film is significantly higher than that of the single layer for YSZ substrates. The five-circle X-ray results show different in-plane orientations for these two bi-layer thin films on MgO and YSZ substrates. The results are also compared with bi-layer thin films grown on well-matched substrates, such as SrTiO3 (a=b=c=0.3905nm).