  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.
