HVY PRECIPITATION IN A TSTM PEELED THE OUTER LAYER FROM AN MLG ACR ACFT.

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FLT DEPARTED PBI OFF RWY 27R WITH RWY HDG DEP. RADAR VECTORS WERE GIVEN UNTIL CLRED DIRECT TO ORLANDO VOR. DUE TO TSTM ACTIVITY OVER CENTRAL FLORIDA; WE REQUESTED TO GO FURTHER R TO AVOID WX; A RTE WE HAD USED IN OUR ARR TO PBI FROM ATL. ATC DECLINED REQUEST BECAUSE OF TFC AND STATED THAT AN ACR FLT HAD JUST FLOWN OUR PRESENT RTE WITH LITTLE TURB OR WX PROBS. WE ACCEPTED THAT AND WERE CLRED DIRECT ORLANDO (HDG 330 DEGS) AND TO CLB TO FL230. PASSING 10000 FT; ALLOWED FLT ATTENDANTS TO GET UP FOR SVC; BUT KEPT SEAT BELT SIGN FOR PAX. OUR RADAR NORMAL SHOWING WX AND SOME CELLS; BUT MOSTLY PRECIPITATION. AT APPROX 14000 FT; TURNED ON ICING PROTECTION DUE TO INDICATIONS ON WINDSHIELD WIPERS INDICATING ICE ACCUMULATION EVEN THOUGH 'RAT' WAS READING PLUS 12 DEGS CELSIUS. PASSING 16800 FT; TOLD BY ATC TO LEVEL OFF AT 17000 FT FOR TFC. SHORTLY THEREAFTER (ABOUT 20 MI LATER) WE ENCOUNTERED HVY PRECIPITATION AND MODERATE TO SEVERE TURB. ALMOST IMMEDIATELY NOTICED SOMETHING LIKE WX STRIPPING PASS OVER WINDSHIELD ALONG WITH PRECIPITATION. ATC FREQ JAMMED WITH TFC AND UNABLE TO GET NEW CLRNC OUT OF WX. AIRSPD FLUCTUATED FROM 270 KTS TO 320 KTS. MAINTAINED FLT CTL AND EVENTUALLY GOT CLB CLRNC TO FL190 AND THEN TO CRUISE ALT. CONDITIONS LASTED FOR ABOUT 2 MINS AND WE WERE ABOUT 50 NM SE OF ORLANDO. RADAR STILL CONTINUED TO WORK NORMALLY. FLT FLEW SAME APPROX RTE BEHIND US; BUT WITH NORMAL CLBOUT AND DIDN'T ENCOUNTER SAME SEVERE CONDITIONS WE HAD. REST OF FLT OPERATED NORMALLY AND UPON LNDG AND PARKING IN ATL; GND MAINT INFORMED US OF SEVERE PRECIPITATION DAMAGE TO RADOME. INSPECTION SHOWED NO OTHER DAMAGE TO ACFT. NO SPARE RADOME AVAILABLE SO FLT CONTINUATION CANCELLED. NO RPTS OF PAX OR FLT ATTENDANT INJURIES. WE FEEL ATC HELPED CAUSE PROB BY DENYING OUR REQUEST TO DEVIATE AS REQUESTED. PROB INTENSIFIED WHEN ATC REQUIRED OUR LEVEL OFF AT 17000 FT FOR TFC FOR A LONG PERIOD OF TIME. ATC WAS SATURATED WITH TOO MUCH TFC AND WX FOR THE CONDITIONS AT THE TIME.