DC3 IN INST CONDITIONS HAS A NEAR MISS WITH A VFR ACFT THAT WAS WORKING WITH CTR FOR TA'S.

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I WAS PLTING A DOUGLAS DC3 ON AN IFR FLT PLAN; LEVEL AT 7000 FT ASSIGNED ALT ENRTE TO MIA. WE HAD BEEN FLYING IN A SOLID LAYER OF CLOUDS WITH VERY LITTLE OUTSIDE VISIBILITY FOR APPROX 5 MINS ABOUT 60 DME NW OF CURVE INTXN; WHEN MY COPLT (PNF) BLURTED OUT IN HORROR THAT HE HAD JUST SEEN ANOTHER ACFT PASSING SLIGHTLY ABOVE AND TO OUR L HEADED IN THE OPPOSITE DIRECTION. I PERSONALLY ONLY SAW A SHADOW; AS I WAS THE PF ON THE INSTS. AT THIS POINT I ASKED ZMA IF THEY HAD ANY OTHER ACFT ON THEIR RADAR SCREEN AT MY 6 O'CLOCK POS AND IN CLOSE PROX. THE CTLR RESPONDED WITH AN AFFIRMATIVE. I THEN RPTED THAT MY COPLT HAD SEEN THIS ACFT AT A DISTANCE OF 50 FT FROM OUR ACFT AS IT PASSED US; AND THAT WE WERE IN IMC FLT CONDITIONS. CHAIN OF EVENTS: HOW THE PROB AROSE: A VFR ACFT; OPERATING IN IMC CONDITIONS WITHOUT AN IFR CLRNC; MANEUVERED RADICALLY; POSSIBLY TO GET BACK INTO VFR CONDITIONS; PASSING WITHIN 50 FT OF MY ACFT IN THE PROCESS. HOW IT WAS DISCOVERED: THE FO PHYSICALLY SAW THE OTHER ACFT PASS US IN VERY LOW IMC CONDITIONS. ZMA VERIFIED ANOTHER ACFT WAS IN OUR VICINITY AT OUR ALT. CONTRIBUTING FACTORS: WX -- CLOUDS; RAIN. CORRECTIVE ACTIONS: THE OCCURRENCE WAS OVER IN LESS THAN 1 SECOND. VISIBILITY WAS POOR; WE COULD NOT HAVE POSSIBLY SEEN THE ONCOMING ACFT ANY SOONER BECAUSE OF THE CLOUDS WE WERE FLYING WITHIN. NO ACTION ON OUR PART COULD HAVE BEEN CONSIDERED. HUMAN PERFORMANCE CONSIDERATIONS: A VFR ACFT FLYING IN LOW IMC CONDITIONS SPEAKS FOR ITSELF. ANY/NO ACTION ON OUR PART WOULD HAVE CHANGED THE OUTCOME. FACTORS AFFECTING THE QUALITY OF HUMAN PERFORMANCE: ZMA WAS WORKING A HIGH NUMBER OF ACFT; INCLUDING THE VFR ACFT INVOLVED; AND MAY HAVE BEEN WORKING TO CAPACITY AT THE TIME. HOWEVER; WITH THE MANEUVER MADE BY THE VFR PLT; IT WOULD HAVE BEEN VIRTUALLY IMPOSSIBLE FOR THE CTLR TO HAVE TAKEN ANY OTHER ACTION. IT ALL HAPPENED TOO QUICKLY.