A B737-300 WAS DISPATCHED IN NON COMPLIANCE WITH THE COCKPIT DOOR ACCESS KEYPAD DEFERRED PER THE MEL. FOUND FORWARD CABIN ATTENDANT'S CREW INTERPHONE INOP. ITEM WAS DEFERRED IN CONFLICT WITH THE MEL.

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IT WAS THE FIRST FLT OF THE DAY AND WE SHOWED UP AT THE ACFT 40 MINS PRIOR TO PUSH. THE ACFT WAS CARRYING AN MEL ITEM FROM THE DAY BEFORE THE FLT. THE MEL WAS THE FLT DECK DOOR ACCESS SYS KEYPAD WAS INOP (MEL 52-17). THE MEL SAID WE WERE GOOD AS LONG AS WE HAD AN OPERATING CREW INTERPHONE SYS. WE PROCEEDED WITH OUR RESPECTIVE PREFLT DUTIES AND THE 'A' FLT ATTENDANT NOTIFIED US OF A PROB THAT HER CREW INTERPHONE SYS WAS NOT WORKING. UPON FURTHER EXAM; WE DISCOVERED HER PA SYS WORKED BUT HER CREW INTERPHONE DID NOT. THE 'B' FLT ATTENDANT INTERPHONE AND PA SYS WORKED NORMALLY AND SO DID OURS IN THE COCKPIT. THE CAPT CALLED DISPATCH AND GOT MAINT ON THE LINE AND INFORMED MAINT AND DISPATCH OF OUR PROB. MAINT GAVE THE CAPT 'MEL 23-4' WITH A TRACKING NUMBER FOR THE FORWARD FLT ATTENDANT CREW INTERPHONE NOT WORKING. DISPATCH FOLLOWED WITH HIS INITIALS AND THE TIME. THE CAPT RETURNED TO THE COCKPIT AND HE REVIEWED MEL 23-4 ON THE OPC. IT LOOKED LIKE WE WERE GOOD TO GO BECAUSE UPON GLANCING AT THE ORIGINAL MEL 52-17; WE INITIALLY FELT THAT SINCE THE COCKPIT AND THE 'B' FLT ATTENDANT CREW INTERPHONE WORKED FINE; WE HAD AN OPERATING SYS. ALSO; WITH DISPATCH AND MAINT BEING IN THE LOOP; WE THOUGHT WE WERE GOOD TO GO. WHILE ENRTE TO ZZZ1 WE REVIEWED THE MEL AGAIN. UPON REVIEW OF THE MEL'S; WE QUESTIONED OUR INTERP OF THE SYS OPERATING NORMALLY AND DECIDED THAT WHEN WE LAND; THE CAPT WOULD CALL DISPATCH AND MAINT AGAIN AND ASK FOR A CLARIFICATION AND RULING ON THIS POINT. UPON ARRIVING; THE NEXT LEG'S PAPERWORK SHOWED BOTH MEL'S BUT THE CAPT STILL CALLED DISPATCH AND MAINT THAT THIS MEL COMBINATION WAS IN FACT OK AND NOT AN OVERSIGHT ON THEIR PART AND NOT A MISINTERP FROM OURSELVES. THE CAPT TOLD ME WHEN HE CALLED MAINT ABOUT THE PROB; THAT THE MAINT PERSON HAD TO ASK ANOTHER MAINT PERSON AND TOGETHER THEY REALIZED IT WAS NOT A LEGAL COMBINATION FOR US TO GO WITH. SO AT THIS POINT WE GOT CONTRACT MAINT IN ZZZ1 TO FIX THE 'A' FLT ATTENDANT CREW INTERPHONE. UNFORTUNATELY; MAINT MISSED THE ILLEGAL MEL COMBINATION AS WELL AS DISPATCH AND WE INITIALLY MISINTERPED THE CREW INTERPHONE MEL. (SO WE; TOO; INITIALLY MISSED IT.)