AN SMA AND AN SMT HAD AN NMAC ON APCH TO LNDG.

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WE DEPARTED MELBOURNE INTL FOR VFR RETURN TO PATRICK AIR FORCE BASE AFTER DOING PRACTICE INST APCHS AT MLB. MLB TWR INSTRUCTED US TO TURN N. WE TURNED N AND CLBED TO 1500 FT AND WERE TOLD 'FREQ CHANGE APPROVED.' WE CONTACTED PATRICK TWR. TWR GAVE US WIND; ALTIMETER; AND SAID 'RWY 02.' WE HAD MADE THE INITIAL CALL-UP AT 6.5 NM OUT. AFTER NO FURTHER INSTRUCTIONS; I ASKED; 'DO YOU WANT US STRAIGHT-IN FOR RWY 02?' TWR REPLIED; 'ROGER;' AND THEN ASKED 'WHAT IS YOUR POS NOW?' I BEGAN REPLYING '5 MI S;' WHEN FROM ABOVE AND L OF US; A MIL SMT DSNDED ALMOST ON TOP OF US AND PASSED US HDG FOR RWY 02. TWR ADVISED; 'ANOTHER ACFT IN THE SAME VICINITY.' ABOUT THIS TIME; THE MIL SMT PLT RPTED 'PASSING OVER TOP OF A GUY BY 100 FT.' TWR SAID NOTHING AND WE BEGAN A 360 DEG TURN FOR SPACING AND WAKE TURB AVOIDANCE. TWR SAID; 'ROGER;' AND AFTER COMPLETING THE 360; INSTRUCTED US TO REMAIN E OF THE RWY FOR LNDG MLT TFC. WE WERE TO FOLLOW THE MLT; #2; CLRED TO LAND. THIS WAS A CLR CASE OF LACK OF COM BTWN THE TWR(S) (MELBOURNE AND PATRICK DUE TO THE CLOSE PROX OF EACH OTHER) AND TFC IN THE PATTERN. WE NEVER SAW THE MIL SMT UNTIL IT APPEARED FROM BEHIND ALMOST ON TOP OF US. NOBODY IN THE TWR(S) CALLED TA'S AND PATRICK TWR SEEMED COMPLACENT AND BEFUDDLED. OUR INITIAL CALL-UP TOOK PLACE AT 6.5 MI FROM THE RWY; LONG ENOUGH FOR TWR TO ADVISE US OF CONFLICTING TFC. THE MIL SMT WAS ON A STRAIGHT-IN ILS; AND ON TWR FREQ. SURELY SOMEBODY IN ATC WENT TO SLEEP ON THIS ONE. WE CALLED THE TWR AFTER LNDG AT PATRICK AND THE TWR SUPVR WANTED TO BLAME THE SMA FOR PASSING THE SMT ON FINAL!!