Air carrier flight crew reported during cruise they encountered severe turbulence which caused them to momentarily lose control of aircraft. They were able to regain control and descended back down to their assigned altitude.

Narrative

Encountered severe Clear Air Turbulence at FL270 out over the Gulf of Mexico. Earlier deviations from weather had brought us south of course. I negotiated a new heading of 065 with JAX Center that would keep us within the 162 NM limit due to the lack of onboard aircraft equipment for ETOPS. It was around XA:20 Zulu that the aircraft violently encountered turbulence and began a rapid climb. The autopilot disconnected and the First Officer (the flying pilot) had stated 'My Aircraft'. As the Pilot Monitoring; I was calling out altitude climb data but with the G loading and airspeed fluctuations and overall shaking of the aircraft with the turbulence it was very hard to gauge a trend. We were basically along for the ride. JAX Center called on frequency with a questionable tone to see if we were ok. I immediately notified the controller we were encountering severe turbulence and trying to get back down to FL270 withy the turbulence and my hand on the mic trigger I had a couple of 'dual Input' audibles and released the trigger. The controller immediately gave us a block altitude and advised we didn't have any traffic near us. The reports to other aircraft started to ensue and the general queries of aircraft damage and injuries to people in the cabin started. We regained control up around FL290 or close to it and were able to descend back down to FL270. During the controlled descent I was able to talk with the flight attendants and ascertain we had no injuries between crew and passengers. We didn't see any aircraft anomaly that would also indicate damage. I reported to JAX Center our condition and then notified dispatch via ACARS what had happened. I was also able to make an entry and make a PA to the passengers. Upon arrival into Miami; I did not see anything abnormal with the condition of the cabin or aircraft. The passengers were in good spirits and very thankful albeit curious to what that actually was. Many appreciated the calming nature of the PA and made mention of it.Cause:a) During the crew brief; I had mentioned that we had two different storm systems that could affect our flight time into Miami with deviations. I physically showed that weather app was indicating areas of a choppy ride in addition to physically showing the WSI (weather app) radar data. I briefed we would most likely be deviating south of Houston before going out over the Gulf. I told them my 'game plan' was to have the service done early (including lavatory breaks and crew meals) before we coast out over water which would be a little over the two hour mark into the flight. As we passed over the Houston area; I called back to the #1 to let her know that it was time to make sure they secured the cabin and took their seats until I could make sure it was going to be ok to do any service or move about. I verified the seatbelt sign ON and continued to mentioned that it would be a while before I could let them back up. I believe this to be the exact thing that kept everyone from getting hurt. They followed my directions and understood my concern. We were lucky a passenger wasn't arbitrarily getting up out of their seat. b) The iPads went flying. The iPad trays were worthless in keeping them secure. The original iPad holders that came with the airplane should have never been removed and replaced with what is essentially a cheap shelf. c) Afterwards; we noticed the weather app didn't show an indication of our turbulence event. Most likely because the iPads had been displaced out of the trays. Still seems odd. Maybe that is something to look into?