Air carrier flight crew reported moderate to severe turbulence resulting in aircraft performance changes during cruise while deviating around thunderstorms. The First Officer reported an airspeed loss and aircraft bank angle warning during the turbulence encounter. The Captain increased speed and requested a lower altitude for smoother ride conditions.

Narrative

While conducting Flight XXXX from ZZZ to ZZZ1 we encountered scattered cells of thunderstorms en route. We chose to request right and left deviations to go through a gap between two cells that ATC was moving traffic through and other aircraft were using to deviate. While almost completely clear of the weather in question; we encountered moderate to severe turbulence. It was more on the side of moderate chop but with it came severe performance changes. We were at 37;000 ft. in IMC. Tops were reported at 42;000 ft. The Captain had sat the Flight Attendants down before we started to deviate; and the seat belt sign was on. So; everyone was seated in preparation for potential weather ahead and stayed seated throughout the incident. While encountering the turbulence we lost and gained up to 20 kts. of airspeed. With full power the airspeed dropped close to and maybe touched the top of the yellow band. It quickly grabbed our attention. I rechecked my app in order to recross check between the app and on aircraft radar. We were clear of any cell by 25 miles. One jerk then caused us to get a roll authority caution in a bank of approximately 40-45 degrees temporarily. We actually increased speed by .01 mach to try to give us more cushion for speed while turning the ignition switches to FLT. The Captain requested a lower altitude to find a better ride while making it easier to maintain speed. ATC was also notified by the Captain while asking for a new altitude. We descended to FL 350 and it gradually got better the farther we got from the weather. Dispatch was notified shortly after as well as Maintenance.