This paper mainly studies the problem of metasurfaces between different mediums. Despite recent advances on metasurfaces, there has been a critical limitation that wave manipulation between two different mediums is theoretically impossible with general approaches since full transmission and desired phase shift cannot be achieved simultaneously. In order to get over this theoretical issue, we propose an asymmetric metasurface that can manipulate waves between two different mediums. By introducing the asymmetry, achieving both full transmission and desired phase shift simultaneously is theoretically enabled. From theoretical approaches, an actual continuum metasurface is designed and applied to various wave manipulations between two different mediums. We expect that the proposed metasurface can be applied to various applications in the area of ultrasonics and vibrations.