A C560 FO DISTRACTED DURING AN EARLY TEB 5 ATC DIRECTED TURN CLBED ABOVE 1500 FT PRIOR TO 4.5 DME. RPTR HAD TUNNEL VISION ON THE TURN.

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TOOK OFF FROM TEB; RWY 24; ON TEB 5 DEP. DEP PROC IS FLY RWY HDG TO 1500 FT; R TURN TO 280 DEGS; MAINTAIN 1500 FT UNTIL 4.5 DME FROM TEB VOR. AFTER TAKEOFF WAS CLBING RWY HEADING; COMING UP ON 1500 FT WHEN CTLR INSTRUCTED BEGIN R TURN TO 280 DEGS; I BEGAN THE R TURN AT APPROX 1350 FT AND BECAME DISTR DURING THE TURN; BECOMING TOO FOCUSED ON BANKING THE ACFT (FOR UNKNOWN REASON) AND ALLOWED THE ACFT; INADVERTENTLY; TO DRIFT ABOVE 1500 FT ALT. I CAUGHT THE ALT AT THE SAME TIME THE CTLR ADVISED 'YOU'RE SUPPOSED TO BE AT 1500 FT.' AND CORRECTED IMMEDIATELY. THE CAPT HAD MADE THE ASSUMPTION THAT SINCE WE WERE TOLD TO TURN BEFORE WE REACHED 1500 FT; THAT WE WERE GOING TO BE CLRED ON UP TO 2000 FT; SO HE DIDN'T CATCH THE ALT DEV EITHER. THIS WAS CAUSED BY INATTENTION ON MY PART AT A CRITICAL TIME. I HAD TUNNEL VISION; ALLOWING MY ATTENTION TO DRIFT AWAY FROM THE BIG PICTURE OF WHAT WAS GOING ON; MICRO MANAGING THE TURNING OF THE ACFT. THE POSSIBILITY OF WHAT COULD HAVE HAPPENED MAKES ME SHUDDER.