<p>Broadband undistorted transmission is one of the criteria to preserve the information carried by incident waves and pulses, allowing imaging formation and source detection. For transmission through artificial materials like metasurfaces, undistorted transmission usually requires each meta-atom to possess exactly the same transmission amplitude and phase. Here, we consider a special acoustic metasurface consisting of meta-atoms with the same transmission phase but different transmittance. Interestingly, we find that when the meta-atoms are of subwavelength scale, the difference in transmittance would not induce substantial distortion in the transmitted wavefront. Based on this observation, we numerically and experimentally demonstrate acoustic metasurfaces that exhibit undistorted transmission and configurable arbitrary reflection. Two distinct types of reflection, i.e., anomalous reflection and diffuse reflection, are numerically and experimentally demonstrated with the transmission wavefront undistorted through a broad spectrum. Our work reveals a more general condition for realizing broadband undistorted transmission and configurable reflection with metasurfaces, which has potential implications in acoustic field manipulation and novel sonar domes.</p>