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In an effort to solve the issue of unadjustable damping of skyhook inertance suspension, a new adjustable device combining an inerter and a damper that aims to simultaneously adjust the inertance and damping was proposed. This article proposes a near practical mathematical model of such an adjustable device, and the model is found to be equivalent to a parallel connection of an adjustable inerter and damper. A prototype of such a device is made, and its damping and inertial forces are separated through quasi-static and dynamic mechanical character tests. The validity of the theoretical models is verified through a comparison between the test and simulation results of the mechanical character with a maximum error of 4.96% for the damping model and 6.28% for the inertial model, which lays the foundation for subsequent studies on adjustable regular patterns of inertance and damping as well as applications in semi-active ISD suspensions. In addition, the device simplifies an inerter and a damper into one device and reduces the layout space and cost, which is of great engineering application value.