ZMA RADAR CTLR TOOK A POINTOUT ON A LEARJET WHO WAS IN ZMA AIRSPACE; DEVIATING AROUND WX; FROM A ZJX CTLR. AT THE SAME TIME THE ZMA CTLR WAS VECTORING AN L1011 AROUND THE SAME WX. THE ZMA CTLR LOST THE LIMITED DATA BLOCK ON THE LEARJET AND DSNDED THE L1011 THROUGH THE LEARJET ALT. THE L1011 GOT A TCASII RA AND FOLLOWED THE RA AND TOLD THE ZMA CTLR WHAT HE WAS DOING. THE L1011 WAS TURNED AND TOLD TO CLB; BUT LTSS OCCURRED.

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DUE TO TSTMS WE WERE DEVIATING W OF COURSE ON A 185 DEG HDG AT FL330. AS WE PASSED A POINT 50 MI W OF PIE; THE WX RADAR SHOWED THAT WE COULD TAKE A TURN TO THE E TOWARD MCO. I CALLED ZMA FOR THE TURN. MIAMI SAID TO MAINTAIN OUR 185 DEG HDG; BUT TO DSND TO FL210. THE CAPT BEGAN THE DSCNT. AT APPROX FL322 IN IMC WE GOT A TCASII RA TO CLB. I TOLD THE CAPT TO CLB. AS HE STARTED TO REVERSE THE DSCNT WE CONTINUED TO GET THE TCASII RA. BY THE TIME WE WERE ABLE TO GET THE PLANE CLBING WE HAD DSNDED TO FL317. ACCORDING TO THE TCASII THE OTHER ACFT PASSED DIRECTLY BENEATH US AT FL310. I TOLD MIAMI THAT WE HAD TFC DIRECTLY BELOW US; MIAMI THEN DIRECTED US TO TURN AND CLB BACK TO FL330. BOTTOM LINE: TCASII SAVED US! SUPPLEMENTAL INFO FROM ACN 344109: A DSCNT OF 1000 FPM WAS STARTED. AT APPROX FL328 TO FL329 THE TCASII GAVE A TA WITH TFC AT FL310 FOLLOWED IMMEDIATELY BY AN RA TO CLB. TCASII FINAL SHOWED A PLUS 700 FT CLOSURE TO CONFLICTING ACFT. CREW CALLED CTR AND ADVISED OF CLB AND WAS INSTRUCTED TO CLB BACK TO FL330 AND TURN 30 DEGS L. CONFLICTING ACFT APPEARED TO PASS DIRECTLY UNDERNEATH ON TCASII; NO VISUAL CONTACT DUE TO CLOUDS. FLT CONTINUED TO MCO AND LANDED WITH NO FURTHER NOTEWORTHY EVENTS. ZMA SUPVR STATED BY PHONE THAT THE CONFLICTING TFC WAS BEING HANDLED BY ZJX; HOWEVER; IT WAS IN ZMA AIRSPACE AND NO HDOF HAD BEEN MADE. SHE FURTHER STATED BY PHONE THAT THIS WAS A CONTINUING PROB BTWN THE 2 CTRS DURING WX DEVS AND HIGH TFC WORKLOADS. SUPPLEMENTAL INFO FROM ACN 344125: RECEIVED A POINTOUT FROM ZJX ON LTT X; A LEARJET; A LIMITED DATA BLOCK; CLBING TO FL310. LTT Y DEVIATED AROUND WX THAT WASN'T PAINTING ON MY SCOPE. I DSNDED ACR X FROM FL330 TO FL210. I DIDN'T SEE THE LIMITED DATA BLOCK (LTT X) WHICH WAS UNDER A FULL DATA BLOCK ON MY SCOPE. BOTH ACFT CAME INTO CONFLICT. CLOSEST PROX WAS 1.2 MI AND 800 FT. NOTE: I WAS UNABLE TO RETRIEVE A FULL DATA BLOCK FOR LTT Y ON MY SCOPE BECAUSE THE FAA IS WITHHOLDING THAT FUNCTION OF THE COMPUTER.