FLC DEVIATED FROM ASSIGNED ALT DUE TO MISTAKEN ATC CLRNC FOR APCH.

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THE FLT HAD BEEN CLRED TO INTERCEPT THE RWY 9L LOC AT 6000 FT AT APPROX 23 MI FROM TOUCHDOWN AT FLL. AT 20 DME AND STILL AT 6 KTS; THE APCH FREQ WAS TOTALLY JAMMED BY A STUCK MIKE IN ANOTHER ACFT. AT THIS TIME WE WERE 'LOST COM' BECAUSE APCH CTLS XMISSIONS WERE TOTALLY UNINTELLIGIBLE. WE WERE VFR. I SWITCHED QUICKLY TO ANOTHER MIA APCH FREQ AND RECEIVED NO ANSWER. DURING THIS TIME; I NOTICED THE COPLT; THINKING HE HAD HEARD A VISUAL APCH CLRNC; BEGIN A SHALLOW RATE OF DSCNT. AT 5900 FT (100 FT LOW); I TOLD THE COPLT TO HOLD HIS ALT. I NEVER HEARD A CLRNC FOR THE VISUAL; BUT WE MAY HAVE BEEN CLRED; WE COULDN'T UNDERSTAND THE FREQ. AT 5700 FT; THE COPLT RECOVERED AND CLBED BACK TO LAST ASSIGNED OF 6000 FT. (A DEV OF 300 FT OCCURRED). I THEN SWITCHED TO TWR AND WE RECEIVED A COORDINATED CLRNC FOR AN UNEVENTFUL APCH AND LNDG AT FLL. TWR RPTED NO PROB AND THAT APCH WAS NOT ABLE TO TALK TO US DUE TO THE INTRUDING STUCK MIKE. THIS IS ONE OF THOSE SITS THAT OCCURS WHEN THERE'S A STUCK MIKE; I BELIEVE WE TOOK TIMELY CORRECTIVE ACTION AND CONDUCTED OURSELVES PROPERLY TO STILL EXECUTE A SAFE; STABILIZED APCH AND LNDG. DURING THE LOST COM WE MAINTAINED; AND WERE VFR.