ALT RESTR ON TETERBORO FOUR DEP NOT COMPLIED WITH.

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CLRED FOR TEB 4 RWY 24 DEP FROM TEB. CAPT; PNF; MISREAD DEP PROC. HE THOUGHT WE WERE TO CLB TO 1500 FT THEN TURN TO 280 DEGS THEN CLB TO 3000 FT. HE SET 3000 FT INTO ALT ALERTER. I DID NOT VERIFY PROC; BUT ASSUMED HE HAD IT CORRECT. ON THE CLBOUT I CONTINUED THE CLB ON 280 DEG HDG TO 1800 FT. AT THIS TIME NEW YORK DEP TOLD US TO MAINTAIN 1500 FT. I LEVELED THE ACFT AND INITIATED A DSCNT FROM 1800 FT TO 1500 FT. WITHIN 2 MINS ATC CLRED US TO 3000 FT. AT NO TIME DID WE GET A TCASII ALERT AND ATC NEVER RPTED ANY TFC. THE REST OF THE FLT WAS COMPLETED AS PLANNED. SUPPLEMENTAL INFO FROM ACN 469222: ON DEP FROM TEB ON THE TEB 4 SID; MY FO WAS FLYING. WE HAD BRIEFED THE SID PRIOR TO TKOF WHICH INCLUDED AN ALT RESTR AT 1500 FT MSL UNTIL 4.5 DME FROM TEB VOR; THEN CLB TO 3000 FT MSL. 3000 FT WAS SET IN THE ALT SELECTOR AS THE ALT CLRED TO. AFTER TKOF; I CONTACTED DEP AND WAS MOMENTARILY DISTRACTED; IT WAS VERY GUSTY AND TURBULENT ON DEP AND MY FO ALLOWED THE ACFT TO CLB THROUGH 1500 FT. I ARRESTED THE CLB AT APPROX 1900 FT MSL AND ADVISED DEP THAT WE WERE LEVELING AT 1500 FT. HE REPLIED THAT WE SHOWED 2000 FT AND HE HAD TFC IN THE AREA. I CONFIRMED 1500 FT AND WE WERE LEVEL WITHIN 10-12 SECONDS. THIS DEP IS USED MOST OFTEN BUT IN A BUSY TERMINAL AREA SUCH AS THIS CAN BE SOMEWHAT BURDENSOME AND DIFFICULT TO NEGOTIATE DURING HIGH TFC AND ATC'S BUSY TIMES. A CONTRIBUTING FACTOR WAS THE LONG DUTY DAY UNTIL ALMOST XA00 AM THAT MORNING -- WE WERE BOTH STILL SOMEWHAT TIRED AND NOT AS SHARP OR FRESH AS A FIRST DAY ON.