MLG CLIMBED ABOVE ALT THAT DEP CTLR SAYS IT WAS CLEARED TO; HANDOFF TO BOS WITHOUT ANY EXPLANATION.

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AFTER TKOF FROM RWY 4 AT BOS; TWR TOLD US TO CONTACT DEP CTL. WE CONTACTED DEP CTL AND HE GAVE US A RIGHT TURN TO A SOUTHERLY HDG; A HIGHER ALT AND SAID TO MAINTAIN SPD 250 KTS. WE TURNED TO HDG 180 DEGS AND SET AND ARMED 15000'. OUT OF APPROX 8000' DEP CTL GAVE US A TURN TO A WESTERLY HDG. I MADE THE TURN AND CONTINUED THE CLB. LEAVING 14000' I REDUCED THE RATE OF CLB TO ABOUT 500 FPM AND REDUCED THE PWR SO AS NOT TO EXCEED THE 250 KT SPD RESTRICTION. AFTER BEING LEVEL AT 15000' FOR ABOUT 1 MIN; THE CAPT RPTED LEVEL AT 15000' IN AN ATTEMPT TO REMIND DEP CTL WE WERE LEVEL AND WOULD LIKE A HIGHER ALT. DEP CTL RESPONDED BY SAYING; 'I ASSIGNED YOU 14000'.' THE CAPT THEN SAID; 'WE WERE GIVEN 15000'.' AGAIN THE CTLR SAID; 'I ASSIGNED YOU 14000'.' THE CAPT THEN SAID; 'WE WERE GIVEN 15000'; WHAT DO YOU WANT US TO DO?' AT THIS POINT I DIDN'T KNOW IF THE CTLR WANTED US TO DESCENDED TO 14000' OR REMAIN AT 15000'. WE DID NOT RECEIVE AN ANSWER FROM DEP CTL. AGAIN THE CAPT ASKED; 'WHAT DO YOU WANT US TO DO?' AT THIS POINT WITH CONCURRENCE FROM THE CAPT I STARTED A GRADUAL DSCNT TO 14000' BECAUSE IT SEEMED TO US THAT IS WHAT DEP CTL WANTED. THE CTLR FINALLY CAME BACK AND SAID; 'CONTACT BOS CENTER (FREQ). THE CAPT SAID; 'BOS CENTER (FREQ).' WE HAD DESCENDED TO ABOUT 14500' WHEN THE CAPT CONTACTED BOS CENTER. CENTER TOLD US TO CLB TO 23000'. THE CENTER CTLR DID NOT QUESTION OUR ALT (14500') WHEN THE CAPT CHKED IN WITH HIM. WE CONTINUED THE FLT W/O FURTHER INCIDENT. I FEEL THE PROB HERE WAS A BREAKDOWN IN COM FROM THE DEP CTLR TO THE FLT CREW ONCE THE CTLR WAS AWARE THAT WE WERE NOT AT THE ALT HE WANTED US AT. AT NO TIME DID THE CTLR QUESTION US ABOUT BEING ABOVE 14000' UNTIL THE CAPT RPTED LEVEL AT 15000'. EVEN AFTER THAT THE CTLR WAS NOT SPECIFIC ABOUT WHAT HE WANTED US TO DO. HE SHOULD HAVE STATED EITHER REMAIN AT 15000' OR DESCENDED TO 14000'. HE LEFT A VERY BIG QUESTION IN OUR MINDS AS TO WHAT HE WANTED.