A B757-200 FLT CREW DESCENDED BELOW CHARTED ALTITUDE ON A NON-PRECISION APPROACH TO MIA.

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FO FLYING; CAPT WAS PLT MONITORING ON THE MIA LOC 8L APCH. FO HAD BRIEFED THAT HE WOULD UTILIZE VNAV SPD INTERVENE DURING THE LOC NON-PRECISION APCH. MIA APCH CLRED US FOR THE VISUAL APCH AND TO CROSS 10 MI W OF MIA AT OR ABOVE 3000 FT; THEN SWITCHED US TO MIA TWR. I ENSURED WE MET THE 3000 FT RESTR WHILE CHKING IN WITH TWR. THEY CLRED US TO LAND #2 BEHIND A LEARJET 4 MI AHEAD. I TOLD THE FO TO CONTINUE TO SLOW WHILE I LOOKED FOR THE TFC. I GUESS I WAS DISTR WHILE LOOKING FOR TFC AND TALKING TO TWR; AND I MISSED THAT THE FO STATED THE AUTOPLT WAS OFF. I DID HEAR WHEN HE ASKED FOR VNAV SPD 140 KTS; BUT I THOUGHT HE WAS MERELY INFORMING ME THAT HE HAD SELECTED IT (BECAUSE I WAS UNDER THE IMPRESSION THE AUTOPLT WAS STILL ON). CONSEQUENTLY; NEITHER OF US SELECTED VNAV. AS WE PASSED THROUGH 3000 FT; I SAID 'I'LL SET 500 FT FOR THE MDA.' AT APPROX 6.5 MI FROM MIA; I NOTICED WE WERE DSNDING THROUGH 1200 FT. I CHALLENGED HIM ON IT AND HE LEVELED AT 1100 FT AND STAYED THERE. MIA TWR CALLED US SHORTLY AFTER THAT STATING; 'LOW ALT WARNING.' BY THAT TIME WE WERE NEARLY BACK ON THE VNAV PATH AGAIN. I FIGURED OUT WHAT HAD HAPPENED; SELECTED VNAV AND THE FO INTERCEPTED THE VNAV PATH AND FLEW THE REST OF THE APCH WITHOUT FURTHER INCIDENT. THE 'LOW ALT ALERT' CALL FROM MIA TWR WAS A SAFETY CALL CONSIDERING WE WERE CLRED FOR THE VISUAL APCH. NEXT TIME I'LL ENSURE I AM BETTER AWARE OF THE AFDS MODE CURRENTLY SELECTED AND THAT WE MAINTAIN AT OR ABOVE THE VNAV PATH ON A VISUAL APCH IF ONE IS AVAILABLE IN THE FMS DATABASE.