LOSS OF SEPARATION BTWN AN ACR B767 CLBING THROUGH 7800 FT AND AN ACR B727 LEVEL AT 8000 FT.

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CLBING OUT OF MIA AFTER TKOF FROM RWY 9L WITH MANY LAYERED CLOUDS AND RAIN SHOWERS IN THE AREA; ZMA GAVE US A CLB FROM 7000 FT MSL TO 16000 FT MSL WHILE WE WERE ON A 360 DEG ASSIGNED HDG FROM MIA DEP CTL. CLBING THROUGH APPROX 7800 FT MSL; I NOTICED A B727 COME OUT OF A CLOUD BANK AT ABOUT 8000 FT MSL HDG W. THE B727 WAS IN OUR 2 O'CLOCK POS ABOUT 2 MI AWAY WHEN I FIRST SAW IT. I LEVELED OFF ABOUT 7900 FT MSL AND MADE JUST A SLIGHT R TURN TO THE E SO I COULD KEEP THE B727 IN SIGHT AND YET PASS BEHIND THE B727. DURING THE SUDDEN; UNPLANNED LEVELOFF AND TURN; THE AIRPLANE EXCEEDED 250 KTS BELOW 10000 FT. ABOUT THE SAME TIME I WAS ALTERING MY FLT PROFILE TO PASS BEHIND THE B727; ZMA GAVE US A NEW COMMAND TO STAY AT 7000 FT. TOO LATE; WE WERE ALREADY AT 7900 FT. WE TOLD CTR THAT WE WERE ALREADY OUT OF 7000 FT AND THAT WE SAW THE B727. ZMA TOLD US TO MAINTAIN VISUAL SEPARATION WITH THE B727; AND AFTER WE ASKED IF WE WERE CLRED TO CONTINUE THE CLB; CLRED US TO CONTINUE OUR CLB TO 16000 FT. I ESTIMATE THE CLOSEST WE CAME TO THE B727 WAS 1 MI. NEITHER ACFT HAD TCASII AND BOTH SHOULD HAVE HAD TCASII. PLEASE MANDATE TCASII ON ALL TRANSPORT CATEGORY ACFT! TELL THE FAA THAT FREIGHT PLTS' LIVES ARE VALUABLE. SUPPLEMENTAL INFO FROM ACN 386837: AT 8000 FT BEING VECTORED HIGH DOWNWIND GOING INTO MIA AT XA00; WE (A CARGO ACFT ON ASSIGNED HDG OF 250 DEGS FOR RWY 12; NON TCASII EQUIPPED) OBSERVED ANOTHER NON TCASII CARGO AIRPLANE GOING SLIGHTLY BEHIND US AT OUR ALT. HE WAS ON AN APPROX 330 DEG HDG AFTER DEPARTING RWY 9L MIA; CLBING OUT. SUPPLEMENTAL INFO FROM ACN 386838: NMAC WITH ACR X ACFT ON DEP HDG APPROX 340 DEGS; OUR HDG 250 DEGS. ATC ADVISED US OF TFC AFTER THREAT WAS OVER. SCATTERED CLOUDS IN THE AREA -- BUSY ATC. ACR X PASSED DIRECTLY BEHIND OUR ACFT. ACFT SEEN AS IT PASSED OUR 9 O'CLOCK POS. CONTRIBUTING FACTORS: 1) OUR ACFT HAD NO OPERABLE MODE C ALT ENCODER (MEL'ED; APPROVED BY ATC). 2) NEITHER ACFT HAD TCASII SYS (ASSUMED IN OTHER ACFT).