CPR LTT; FL370; ENCOUNTERED CUMULUS CLOUD TOPS RESULTING IN ALTDEV TO FL355 AND ON RETURN OVERSHOT ALT TO FL375. FLC WAS PROGRAMMING FMS FOR APCH TO MSY.

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FLYING LEVEL ON AUTOPLT AT FL370; BOTH PLTS HAD HEAD DOWN WHILE PROGRAMMING THE FMS FOR THE STAR INTO MSY. AFTER PROGRAMMING THE FMS; WE LOOKED UP TO SEE WE WERE APPROX 1000 FT BELOW THE TOP OF A CELL. IT WAS TOO LATE TO TURN. WE TURNED ON THE FASTEN SEAT BELTS LIGHT AND ENTERED THE CLOUD. WE EXPERIENCED MOSTLY MODERATE TURB. THE ACFT PITCHED DOWN AND EXCEEDED MMO. PWR WAS REDUCED AND THE AUTOPLT KICKED OFF. ACFT PASSED THROUGH CLOUD AND STABILIZED AT APPROX FL355. WE INITIATED A CLB TO RETURN TO FL370 AND RE-ENGAGED THE AUTOPLT. AT FL370 THE AUTOPLT FAILED TO CAPTURE ALT. PRESELECT AND CORRECTIVE ACTION WAS TAKEN. ACFT CLBED TO FL375 BEFORE STARTING ITS DSCNT BACK TO FL370. THE RADAR DID NOT SHOW ANY RETURNS ON THIS CLOUD FORMATION. OUR TCASII WAS OPERATIONAL AND DID NOT GIVE ANY TFC ALERTS. THIS WAS THE FIRST TIME I HAVE EXPERIENCED A SIGNIFICANT ALT LOSS IN TURB AND I WOULD HIGHLY SUGGEST AVOIDING CLOUDS AT ALT WHEN POSSIBLE. AFTER INITIAL UPSET AND RECOVERY; GREATER DILIGENCE MUST BE PAID TO THE FLT DIRECTOR AND AUTOPLT TO INSURE PROPER SETUP AND CAPTURE OF ALT PRESELECT.