Aims: we studied the global distribution and kinematics of the extra-planar neutral gas in the Milky Way. Methods: we built 3D models for a series of Galactic HI layers, projected them for an inside view, and compared them with the Leiden-Argentina-Bonn 21-cm observations. Results: we show that the Milky Way disk is surrounded by an extended halo of neutral gas with a vertical scale-height of 1.6[+0.6/-0.4] kpc and an HI mass of 3.2[+1.0/-0.9]x10^8 solar masses, which is 5-10% of the total Galactic HI. This HI halo rotates more slowly than the disk with a vertical velocity gradient of -15[+/-4] km/s/kpc. We found evidence for a global infall motion, both vertical (20[+5/-7] km/s) and radial (30[+7/-5]km/s). Conclusions: the Milky Way HI halo shows properties similar to the halos of external galaxies and is compatible with being predominantly produced by supernova explosions in the disk. It is most likely composed of distinct gas complexes with masses of 10^4-10^5 solar masses of which the Intermediate Velocity Clouds are the local manifestations. The classical High Velocity Clouds appear to be a separate population.