A320 FLT CREW ENTERS MODERATE TURB; AND THE ACFT EXCEEDS ITS MAX MACH OPERATING SPD (MMO); CAUSING THE AUTOFLT SYS TO ATTEMPT TO REDUCE THE SPD.

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DURING CRUISE AT FL350; WE EXPERIENCED OCCASIONAL LIGHT CHOP IN IMC. THE ONLY WX ON OUR RADAR WAS APPROX 40 MI AHEAD AND SLIGHTLY R OF COURSE. THE CAPT ASKED AND RECEIVED CLRNC FOR DIRECT VRB TO PROVIDE GREATER DISTANCE FROM WX (CELL) AT OMN. SUDDENLY; WE ENTERED MODERATE TURB. THE CAPT BEGAN REDUCING SPD TO .76 MACH (NORMAL CRUISE WAS .80 MACH). AS TURB INCREASED; AN OVERSPD OCCURRED. THE AUTOMATIC OVERSPD PROTECTION FOR THE AIRBUS 320; THE AUTOPLT DISENGAGES; AND A PICK-UP IS COMMANDED TO REDUCE AIRSPD. THE PLT IS UNABLE TO OVERRIDE PITCH-UP COMMAND UNTIL AIRSPD IS BELOW MMO/VMO. THE ACFT CLBED OVER 3000 FT IN 20-30 SECONDS WITH AIRSPD IN THE BARBER POLE UNTIL ABOVE FL380. AT THAT TIME; THE CAPT WAS ABLE TO CTL ACFT PITCH. HE LEVELED AT FL380. I HAD MADE CALLS TO JACKSONVILLE CTR DURING THE UNCTLED CLB. THE CTLR ANSWERED WHEN THE ACFT LEVELED AT FL380 (APPROX 30 SECONDS AFTER THE ACFT CLB STARTED). THEN ZJX ISSUED CLRNC TO FL370 AND ADVISED US THAT THERE WERE NO OTHER ACFT IN AREA. AS THE CAPT LEVELED THE ACFT TO FL380; THE AIRSPD REDUCED TO VLS AND THEN STABILIZED AT .76 MACH. THE ZJX CTLR RPTED THAT THERE WAS NO WX WITHIN 20 MI OF ACFT ON HIS RADAR SCREEN. THE REMAINDER OF FLT WAS NORMAL. I BELIEVE THAT WE ENTERED A BUILDING CELL WITHOUT RADAR RETURN; BECAUSE OF SUDDEN TURB AND THE RATE OF CLB. WE ENTERED AN UPDRAFT WHILE THE AUTOPLT WAS HOLDING LEVEL AT FL350. THEN THE OVERSPD OCCURRED. THE AUTO PROTECTION ALONG WITH THE UPDRAFT; CAUSED THE ACFT TO CLB 3000 FT. WE WERE SURPRISED BY THE SUDDEN OVERSPD AND THE CLB RATE AT FL350.