We consider the problem of a diblock copolymer thin film melt on a striped surface. The striped surface induces the lamellae to orient perpendicularly to the surface and align commensurate with the stripes at the bottom of the film. In all practical cases at the top of the thin film the free surface will prefer one block compared to the other block. This can cause the lamellae to distort to accommodate the interfacial tension difference. We study this distortion theoretically and show it will always occur but that the amplitude is usually small. We also compare this morphology with a mixed surface morphology to determine which morphology will be observed as a function of film thickness and surface tensions.