Learjet 60 Captain reported aircraft loss of pitch and roll control at 41,000 ft., resulting in a loss of altitude. The Captain disconnected the automation to recover the aircraft at 38,500 ft. and received course changes from ATC. Once in smoother air, without aircraft damage or injuries, the flight continued to destination.

In cruise flight on top of overcast our aircraft experienced a shudder and sudden pitch down. The autopilot was still engaged, the rate of descent we estimated at about 10,000 feet per minute with pitch and roll oscillations. I disconnected the autopilot and attempted to stop the altitude loss. The aircraft stabilized after an altitude loss of 2,500 feet at FL385. All this time we were communicating a loss of control with Center, which cleared us block altitudes of FL370-410 as necessary. There was a few minutes of smoother air then a sudden updraft of 6,000 feet per minute with power at idle and wild airspeed fluctuations +- 20 kts as I was fighting pitch and speed variations. We were able to return to FL410 after two course changes towards the South East of our route. Center had advised another aircraft at FL450 had reported extreme turbulence estimated 50 NM north of us and another aircraft at FL310 was also diverting because of turbulence. Our on board radar indicated we had a level 5 cell tops FL500 at 35 miles north of our route. Center advised our track was in between a few small cells and looked good. We concurred. In debrief after the flight we agreed that our filed route should have been above the reported weather in the small portion of our route that there was any showing and the route changes we made may have prevented us from transiting even worse conditions. Prompt communications with ATC helped get course and altitude changes certainly helped prevent any injuries and airframe damage. I don't know what else we could have done.