Air carrier Captain reported during the climb encountering turbulence resulting in loss of control of the aircraft. The flight crew regained control of the aircraft and proceeded to their destination.

Narrative

After checking on with center; center advised that 310 was a good ride and 33 and 35 were turbulent which corresponded to what the forecast looked like on the FD pro Wx outlook. When we were level for less than a minute; turbulence started getting light to moderate. PM called in the back to have the crew take their jump seats. A few moments later; aircraft started to undergo severe turbulence; loosing partial control of the autopilot capabilities; and descending 400 feet in about 45 seconds time; then climb back up and exceed altitude by 200 feet and then settle back down to level. after a few seconds; the turbulence came back; and we requested FL290 and an immediate descent. PF/FO tried to descent with the autopilot engaged; however the vs was fluctuating +- 200-400 FPM and wouldn't descend so CA/PM took controls and descended manually without Ap on to 290.. Informed ATC and they asked for any damage or injury; and I replied no after getting a report from the FA. No further actions taken and no diversion was needed for Passenger safety. continued to ZZZ as filed.