AN ACR DEPARTING MIA WAS BEING VECTORED FOR WX AND CLRED TO 6000 FT. AT 6000 FT TRACON ADVISED CLRNC WAS TO 5000 FT AND FLT DESCENDED.

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CLRNC FOR TKOF RWY 08R MIA. TWR HAD ADVISED WE WILL MAKE A 180 HDG TO AVOID TSTMS. WIND WAS 030/22 KTS. AFTER TKOF; WE TURNED TO OUR INITIAL HDG OF 180 DEGS. UPON HDG 180; WE HAD THE RADAR DEPICTING WX ON THIS HDG. WE REQUESTED 200 DEG HDG. UPON RECEIVING THE 200 DEG HDG; DEP CTL STOPPED OUR CLB TO 3000 FT FOR TFC. LEVELING AT 3000 FT; WE KEPT THE ACFT AT 230 KTS. NEXT DEP CLRED US TO CLB TO 6000 FT. I; AS CAPT; REPEATED 6000 FT DIALED IN THE ALT AND HAD THE FO VERIFY 6000 FT; WHICH WE HAD REPEATED; AND WE STARTED OUR CLB TO 6000 FT. ONCE LEVEL AT 6000 FT; THE DEP CTL SAID WE WERE CLRED TO 5000 FT AND NOW WE NEEDED TO TURN TO A HDG OF 130 DEGS. WE RESPONDED WITH A TURN TO 130 AND DESCENDING TO 5000 FT. DURING THE TURN AND THE DESCENT; ATC CALLED BACK WITH A 100 DEG HDG. WE INITIATED THE TURN AND DESCENT IMMEDIATELY. ONCE LEVEL AT 5000 FT AND HDG 100 DEGS; WE WERE CLRED TO CLB TO 16000 FT. NO RA'S OR TA'S.SUPPLEMENTAL INFO FROM ACN 754736: CONTRIBUTING FACTORS: DUE TO WX EAST OF THE FIELD; WE WERE GIVEN A DEP HDG OF 180 DEGS. WE ALSO HAD INSTRUCTIONS TO LEVEL AT 3000 FT VICE 5000 FT. WHILE GIVING US CLRNC TO 6000 FT; THE DEP CTLR MENTIONED TFC. PERHAPS HE MEANT TO SAY CLB TO 5000 FT DUE TO TFC AT 6000 FT. THE WX WAS A FACTOR AFFECTING ARRS; DEPS AND CTLRS.