B737-700 Captain reported severe turbulence resulting in altitude and airspeed exceedances. The Captain took control and stabilized the aircraft after descending out of the turbulence.

Narrative

Approximately one hour into our flight from ZZZ1 to ZZZ we encountered light; occasional moderate chop at FL410. The chop intensity increased resulting in airspeed fluctuations resulting in an over speed and clacker activation. At this point; I contacted the Flight Attendants; had them take their seats and requested a descent to FL390 from ATC. The descent to FL390 put us in the tops of the weather system we were passing over en route. At this point in the flight ATC only reported light to occasional chop all altitudes in the vicinity of the front. Due to MEL XX-XX-XX (Wi-Fi INOP) applying to this aircraft/flight the additional information provided by SkyPath; WSI; and/or Jeppesen was not available to us. Suddenly; and without any visual indications externally or on our radar display; we encountered severe turbulence at FL390.Initial altitude fluctuations exceeded plus/minus 500'; and rapid airspeed changes resulting in both an over speed indication (clacker activation) and a low-speed indication (stick shaker activation) were experienced. While the First Officer (PF) was attempting to stabilize airspeed and altitude (autopilot engaged); I (PM) reported the severe turbulence encounter to ATC; stating that we were unable to maintain altitude and requested a descent to FL350. After receiving descent clearance; I entered FL350 in the altitude window; selected Level Change and directed the First Officer to descend. At this point the autopilot and aircraft failed to respond to the altitude change input. I assumed control of aircraft; disconnected the autopilot; and initiated the descent to FL350. Once stabilized and level at FL350; I transferred control back to the First Officer. I then proceeded to contact the Flight Attendants to check for injuries; further advised ATC of the aircraft status; and advised Dispatch/Maintenance through ACARS of the turbulence encounter. Upon landing in ZZZ; both the severe turbulence and exceedance were entered in the logbook. A conference call with Dispatch; Supervisor on Duty; Maintenance; and Chief Pilot Dispatch was initiated; and a severe turbulence ground inspection was completed with no defects found. Preventative Measures: Had the Wi-Fi been working; additional information concerning turbulence reports and weather information may have been available and assisted us in either avoiding or at least preparing for the turbulence encounter.