For the first time, we have studied the rich internal structure of a magnetosheath high‐speed jet. Measurements by the Magnetospheric Multiscale (MMS) spacecraft reveal large‐amplitude density, temperature, and magnetic field variations inside the jet. The propagation velocity and normal direction of planar magnetic field structures (i.e., current sheets and waves) are investigated via four‐spacecraft timing. We find structures to mainly convect with the jet plasma. There are indications of the presence of a tangential discontinuity. At other times, there are small cross‐structure flows. Where this is the case, current sheets and waves overtake the plasma in the jet's core region; ahead and behind that core region, along the jet's path, current sheets are overtaken by the plasma; that is, they move in opposite direction to the jet in the plasma rest frame. Jet structures are found to be mainly thermal and magnetic pressure balance structures, notwithstanding that the dynamic pressure dominates by far. Although the jet is supermagnetosonic in the Earth's frame of reference, it is submagnetosonic with respect to the plasma ahead. Consequently, we find no fast shock. Instead, we find some evidence for (a series of) jets pushing ambient plasma out of their way, thereby stirring the magnetosheath and causing anomalous sunward flows in the subsolar magnetosheath. Furthermore, we find that jets modify the magnetic field in the magnetosheath, aligning it with their propagation direction.