CITATION X FLT CREW OVERSHOOTS REQUIRED ALT ON THE TEB 5 DEP. CTLR QUERIED FLT CREW AS TO THEIR ALT; ISSUED NEW CLRNC.

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OUR CLRNC WAS THE TEB 5 DEP OFF OF RWY 24 FROM TEB. I WAS THE PF IN THE L SEAT; THE PIC WAS THE PNF IN THE R SEAT. WE BRIEFED THE PROC WHEN IT WAS RECEIVED APPROX 30 MINS PRIOR TO SCHEDULED DEP. PAX WERE AN HOUR LATER THAN EXPECTED. AFTER THE PAX ARRIVED WE DID NOT FULLY REBRIEF THE SID; ONLY THE INITIAL ALT (1500 FT) AND THE REQUIRED TURN TO A HEADING OF 280 DEGS. I MISINTERPRETED THE PROC AS REQUIRING A TURN AT 1500 FT AND A CONTINUATION OF THE CLB TO THE ASSIGNED ALT (8000 FT). AFTER TAKEOFF AND REACHING 1500 FT I BEGAN THE TURN TO THE NEW HEADING AND CONTINUED THE CLB. THE PNF CALLED OUT 1500 FT BUT I CONTINUED CLB UNTIL HE SAID I NEEDED TO STOP AT 1500 FT. I LEVELED AT 2300 FT. ATC QUERIED US ON OUR ALT AND WE TOLD THEM WE WERE RETURNING TO 1500 FT. THE CTLR TOLD US TO MAINTAIN OUR ALT BECAUSE THERE WAS ANOTHER ACFT AT OUR 9 O'CLOCK POSITION. WE DID NOT SEE THE ACFT NOR WAS THERE ANY TCAS ALERT. AFTER A MOMENT THE CTLR CLRED US TO CLB AND GAVE US A PHONE NUMBER TO CALL. THE WEATHER WAS CLR. CONTRIBUTING FACTORS WERE OUR FAILURE TO FULLY REBRIEF THE SID AFTER THE DELAY; MY FIXING IN MY MIND THAT 1500 FT WAS ONLY AN ALT TO BEGIN THE TURN TO THE NEW HEADING AND NOT A MANDATORY ALT TO STOP AT; FAILURE TO SET THE ALT ALERTER AT 1500 FT; AND THE PNF NOT BEING MORE ASSERTIVE IN CALLING OUT THE ALT. SHORTLY AFTER THE EVENT; THE PNF AND I REVIEWED THE ENTIRE EVENT WITH THE COMPANY. THE COMPANY PROCS WILL BE REVIEWED TO IMPROVE BRIEFING REQUIREMENTS FOR ALL SIDS/STARS. SUPPLEMENTAL INFO FROM ACN 690102: AS WE CLBED THROUGH 1400 FT; I COULD SEE THAT WE WERE CLBING AT A RATE THAT WOULD NOT ALLOW A NORMAL LEVELOFF AT 1500 FT. I SAID TO THE FLYING PLT; 'YOU ARE COMING UP ON 1500 FT.' THE FLYING PLT RESPONDED 'I GOT IT.' HOWEVER; HE DID NOT BEGIN A LEVELOFF AND I ONCE AGAIN STATED THAT WE WERE APPROACHING 1500 FT. AGAIN HE STATED 'OK; I GOT IT.' AS THE ACFT CLBED THROUGH 1500 FT; I SAID; 'NO; WE NEED TO LEVEL AT 1500 FT.'