Wideband millimeter-wave communication systems can be extended to provide radar-like sensing capabilities on top of data communication, in a cost-effective manner. However, the development of joint communication and sensing technology is hindered by practical challenges, such as occlusions to the line-of-sight path and clock asynchrony between devices. The latter introduces time-varying timing and frequency offsets that prevent the estimation of sensing parameters and, in turn, the use of standard signal processing solutions. Existing approaches cannot be applied to commonly used phased-array receivers, as they build on stringent assumptions about the multipath environment, and are computationally complex. We present JUMP, the first system enabling practical bistatic and asynchronous joint communication and sensing, while achieving accurate target tracking and micro-Doppler extraction in realistic conditions. Our system compensates for the timing offset by exploiting the channel correlation across subsequent packets. Further, it tracks multipath reflections and eliminates frequency offsets by observing the phase of a dynamically-selected static reference path. JUMP has been implemented on a 60 GHz experimental platform, performing extensive evaluations of human motion sensing, including non-line-of-sight scenarios. In our results, JUMP attains comparable tracking performance to a fullduplex monostatic system and similar micro-Doppler quality with respect to a phase-locked bistatic receiver.