We present a study of full-wave tailoring with an elastic metasurface between two different media. Unlike previous research on elastic metasurface, the current study has a crucial difference that the metasurface is placed between two different media. Interestingly, we find that previous studies have a theoretical limitation that negates the simultaneous achievement of various phase shifts and full transmission between inhomogeneous media. To overcome this, we propose a double-unit elastic metasurface composed of two units, phase modulator and impedance matcher, to avoid the constraint restricting various phase shifts with full transmission. Numerical and experimental investigations are performed to validate the operation of the double-unit elastic metasurface. The proposed metasurface is expected to be applied in various ultrasonic applications.