A LJ35 DEPARTING ON THE TEB 5 DEP EXCEEDED THE INITIAL 1500 FT LEVEL OFF ALT BY 300 FT.

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WE DEPARTED TEB ARPT RWY 24. THE DEP INSTRUCTIONS WERE TO MAINTAIN RWY HDG UNTIL REACHING 1500 FT; THEN TO TURN R TO A HDG OF 280 DEGS. AT THE TEB VOR 4.5 DME; WE THEN WERE SUPPOSED TO CLB TO 2000 FT FOR RADAR VECTORS TO OUR ASSIGNED RTE. I WAS THE CAPT ON THE TRIP AND WAS FLYING WITH A CONTRACT CO-PLT WHO HAD BEEN A CAPT WITH MY COMPANY A FEW YEARS EARLIER. THE CO-PLT WAS THE PLT FLYING AND WAS IN THE L SEAT. I HAD BRIEFED HIM TWICE ON THE DEP INSTRUCTIONS; PRIOR TO TKOF. I HAD ALSO BRIEFED HIM THAT I WOULD 'BUG' AND 'SELECT' THE HDGS AND ALTS AT THE APPROPRIATE TIMES. AFTER DEPARTING RWY 24 WE CLBED TO 1500 FT. AT REACHING 1500 FT THE CO-PLT ASKED ME WHAT HDG TO TURN TO. I TOLD HIM 280 DEGS AND SELECTED THAT HDG WITH HIS HDG BUG. I LOOKED DOWN AT THE DEP PLATE TO VERIFY THE HDG AND AS I DID THE CO-PLT CLBED THE AIRPLANE TO 1800 FT. AFTER HE WAS ALREADY AT THIS ALT HE ASKED ME IF HE NEEDED TO BE AT 2000 FT TO WHICH I IMMEDIATELY RESPONDED 'NO!' I INSTRUCTED HIM TO DSND BACK DOWN TO 1500 FT. HE HAD ALREADY INITIATED THE TURN TO 280 DEGS BUT WAS SLOW TO CORRECT HIS ALT. WE WERE ONLY AT THIS 1800 FT ALT FOR 10 TO 20 SECONDS WHEN ATC CALLED AND INFORMED US THAT WE NEEDED TO BE AT 1500 FT UNTIL 4.5 DME. THEY DIDN'T INFORM US OF ANY TFC CONFLICTS AND ALMOST IMMEDIATELY ASSIGNED US A HIGHER ALT. THE REST OF THE FLT WAS WITHOUT INCIDENT.