CRJ700 flight crew reported loss of aircraft control in severe turbulence and a decision to divert.

Narrative

Cruising at FL 340 we started to encounter heavy moderate chop. We asked for FL 320 and shortly after ATC cleared us down to FL 320. As we descended; the aircraft was banking 20-30 degrees and the turbulence got severe. Captain (CA) then took the autopilot off. They were not able to maintain altitude at 320 and we told ATC we needed to go lower. ATC said standby; we decided we needed to advise ATC and kept descending. ATC told us to maintain FL 280 right before we were able to call and request. ATC then cleared us a block altitude from FL 290 to FL 260. The turbulence went back to moderate chop right at FL 280 and we were able to maintain altitude. The CA then reengaged the autopilot. CA looked visibly stressed from the encounter. About 5 mins later the CA said they don't want to continue and they wanted me to take over as Pilot flying (PF) and divert. We decided to divert to ZZZ. We then swapped the autopilot over to the First Officer's (FO's) side and FO took flight controls. CA handled all the PM duties. We had to be vectored around for about 5 mins before the approach to burn 500 lbs. of fuel in order to land below max landing weight. We had not heard any reports of moderate turbulence around us. We did know thunderstorms were passing South of our path earlier in the day. PF could have advised ATC earlier when we knew we were having trouble maintaining altitude. Severe turbulence caused us to decide to divert.