A HAWKER HS125 DEPARTING TEB ON THE TEB DEP FAILED TO LEVEL OFF AT THE CHARTED 1500 FT RESTR; CLBING TO 1800 FT; AT LEAST PARTLY BECAUSE OF A TCAS TA.

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WE WERE DEPARTING TEB AT THE START OF RUSH HOUR ON RWY 24 ASSIGNED THE TEB 5 DEP. THE TEXTUAL DESCRIPTION SAYS TO FLY RWY HEADING UNTIL REACHING 1500 FT THEN FLY HEADING 280. MAINTAIN 1500 FT UNTIL 4.5 DME FROM TEB THEN CLB TO 2000 FT. WE HAD AMPLE TIME TO DISCUSS THE DEP SINCE WE WERE ABOUT NUMBER 7 FOR DEP AND ELECTED TO SET 2000 FT IN THE ALT ALERTER. TKOF WAS NORMAL WITH A NOISE ABATEMENT CLB EXECUTED. JUST AFTER GEAR AND FLAPS WERE RETRACTED; CLBING THROUGH ABOUT 1000 FT; WE GOT A TFC ALERT FROM THE TCAS. BOTH CREWMEMBERS LOOKED OUTSIDE FOR THE TFC. I MADE THE HEADING CHANGE TO 280 DEGS; BUT DID NOT LEVEL AT 1500 FT DUE TO THE TFC DISTRACTION. I NOTICED MY ERROR AT 1800 FT AND PUSHED OVER TO DESCEND JUST AS DEP CTL CALLED TO TELL US TO WATCH OUR ALT. WE LEVELED AT 1500 FT AND RESUMED THE DEP AS REQUESTED. I WAS GIVEN A TELEPHONE NUMBER TO CALL UPON ARR AT DEST. CONTRIBUTING FACTORS: 1) HIGH TFC; HIGH WORKLOAD ENVIRONMENT. THIS DEP REQUIRES A NOISE ABATEMENT CLB WITH A TURN AND LEVEL OFF AT 1500 FT MSL. 2) PART TIME FO WHOM I FLY WITH ON A SPORADIC BASIS. 3) WE HAD EXPERIENCED A RESOLUTION ADVISORY (RA) FROM THE TCAS ON THE ARR 3 HOURS EARLIER AND HAD TAKEN EVASIVE ACTION TO AVOID A COLLISION WITH AN ACFT ATC WAS NOT TALKING TO. WE WERE 'SPRING LOADED' TO TCAS ALERTS FROM THE CLOSE CALL A FEW HOURS EARLIER. BOTH OF US SHOULD NOT HAVE LOOKED OUTSIDE THE COCKPIT AT THE SAME TIME DURING THIS HIGH WORKLOAD PHASE OF FLT. THE INITIAL ALT OF 1500 FT SHOULD HAVE BEEN SET IN THE ALT ALERTER INSTEAD OF 2000 FT. BOTH CREW MEMBERS SHOULD HAVE BEEN MORE DILIGENT IN ALT MONITORING. WE WERE NOT FATIGUED FROM A LONG DAY; BUT HAD BEEN IN A HIGH STRESS; HIGH WORKLOAD ENVIRONMENT ALL DAY HAVING COME FROM THE WASHINGTON; DC; AREA TO THE NEW YORK AREA.