BE40 CREW HAD AN ACFT UPSET AFTER GETTING TOO CLOSE TO A TSTM IN ZJX CLASS A.

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I WAS THE CAPT OF A BE40 ON MAY/SUN/03; TRAVELING FROM TEB TO BCT ON AR1; 75 MI N OF HOBEE INTXN. WE WERE AT FL390 IN IMC CONDITIONS; IN CRUISE WITH THE AUTOPLT ENGAGED. AN AREA OF TSTMS WAS BEING DEPICTED ON WX RADAR ABOUT 50 MI AHEAD. A DEV L OF COURSE WAS REQUESTED AND RECEIVED FROM ZJX. WHILE DEVIATING; WE ENCOUNTERED A BUILDUP THAT WAS NOT DEPICTED ON RADAR. HEAVY RAIN AND SEVERE TURB WERE ENCOUNTERED RESULTING IN THE AUTOPLT DISENGAGING; THE ACFT BEING ROLLED L 45 DEGS; AND A LOSS OF 1200 FT. THE ACFT WAS RECOVERED BACK TO FL390; AND THE ENTIRE SCENARIO TOOK LESS THAN 1 MIN. ZJX DID NOT QUESTION THE ALTDEV; AND EVEN THOUGH I DID NOT THINK I COULD BE VIOLATED FOR AN ALTDEV DUE TO WX; I DID NOT RELAY THE ENCOUNTER TO ZJX. I SEE NO WAY IN WHICH IT COULD HAVE BEEN AVOIDED; SINCE WE COULD NEITHER SEE IT VISUALLY OR SEE IT ON RADAR. I DO; HOWEVER; THINK MY SIC WAS SLOW TO REACT; AND THAT SOME OF THE ALT LOSS COULD HAVE BEEN AVOIDED WITH QUICKER RESPONSE TO THE UNUSUAL ATTITUDE. IN HINDSIGHT; I SHOULD HAVE ASSUMED CTL OF THE ACFT AS THE PNF; AND RECOVERED THE ACFT BACK TO FL390 QUICKER. THERE WERE NO INJURIES TO PAX OR CREW; AND NO DAMAGE TO THE ACFT. ALL OF THE RADAR DEPICTED TSTMS WERE AVOIDED AND THE REST OF THE FLT WAS UNEVENTFUL. ACFT LANDED AT BCT WITHOUT FURTHER INCIDENT.