Air taxi First Officer reported severe turbulence caused a temporary loss of control and altitude excursion.

Narrative

I was a pilot monitoring for the flight from ZZZ to TEB. As we were at the end of LVZ5 arrival;NY Approach vectored us off the arrival and instructed to descend from 6000' to 3000'. Next ATC instruction was to fly direct SKUBY intersection; and cross SKUBY at 3000'. Numerous aircraft landing at TEB around this time reported severe turbulence on initial descent and approach to Teterboro. This was also added to the ATIS report.On LVZ5 arrival we experienced moderate turbulence; all the way. On descent from 6000' to 3000' turbulence become severe; to the point where it was difficult and occasionally impossible to control the aircraft. At altitude of around 3200';with Autopilot engaged and vertical speed mode; 1000/fpm descent set; aircraft ascended to 3600' ;and Autopilot disengage. ATC asked us what's the reason for the climb; I reported severe turbulence and we corrected the altitude. In my flying career; I have never experienced such of phenomena and intensity of turbulence.Diversion to different airport in this situation could be a much better choice; instead of landing at Teterboro. Lesson learned.