We present the results of deep Chandra and XMM-Newton X-ray imaging and spatially-resolved spectroscopy of Abell 2256, a nearby (z=0.058) galaxy cluster experiencing multiple mergers and displaying a rich radio morphology dominated by a large relic. The X-ray data reveals three subclusters: (i) the `main cluster; (ii) the remnant of an older merger in the east of the cluster with a ~ 600 kpc long tail; (iii) a bright, bullet-like, low-entropy infalling system, with a large line-of-sight velocity component. The low-entropy system displays a 250 kpc long cold front with a break and an intriguing surface brightness decrement. Interestingly, the infalling gas is not co-spatial with bright galaxies and the radio loud brightest cluster galaxy of the infalling group appears dissociated from the low entropy plasma by 50 kpc in projection, to the south of the eastern edge of the cold front. Assuming that the dark matter follows the galaxy distribution, we predict that it is also significantly offset from the low-entropy gas. Part of the low frequency radio emission near the cold front might be revived by magnetic field amplification due to differential gas motions. Using analytical models and numerical simulations, we investigate the possibility that the supersonic infall of the subcluster generates a large scale shock along our line-of-sight, which can be detected in the X-ray temperature map but is not associated with any clear features in the surface brightness distribution.