AN LR60 FLT CREW DEVIATED FROM THE CHARTED ALT RESTRS ON THE TEB DEP OUT OF TEB.

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AFTER COMPLETION OF A VERY RUSHED QUICK TURN WE STARTED ENGINES AND BEGAN A TAXI TO RWY 24 AT TEB. WE HAD BEEN ASSIGNED THE TEB 5 DEP. AS I HAD FLOWN IN AND OUT OF TEB FREQUENTLY AND FELT VERY COMFORTABLE WITH THE VARIOUS DEPS I ASKED THE FO TO READ THE TEB 5 DEP TO ME DURING THE TAXI OUT TO THE RWY. THE FO READ THE PROC TO ME AND I REPEATED IT BACK. WE TOOK OFF FROM RWY 24 ON RWY HEADING AND WHILE PASSING THROUGH 1500 FT I BEGAN A TURN TO 280 DEGS. ALMOST IMMEDIATELY THE DEP CONTROLLER CALLED AND TOLD US TO REMAIN AT 1500 FT. I WAS PROBABLY PASSING 1700 FT AND I STOPPED CLBING AND BEGAN A DESCENT TO 1500 FT. THE CTLR CALLED US AGAIN AND TOLD US WE HAD NOT BEEN PROPERLY FOLLOWING THE TEB 5 DEP AND TO MAKE SURE TO TURN ON THE 280 DEG HEADING. THE CTLR SUBSEQUENTLY CLRED US TO A HIGHER ALT AND DIFFERENT HEADING AND THEN PASSED US TO ANOTHER FREQUENCY WITHOUT FURTHER INCIDENT. WHEN THE CTLR FIRST CALLED TO WARN OF OUR DEVIATION I WAS EXTREMELY CONFUSED BECAUSE I THOUGHT WE WERE FOLLOWING THE PROPER PROC. IN CRUISE I HAD TIME TO LOOK AT THE TEB 5 DEP AGAIN AND DETERMINE WHAT HAD GONE WRONG. IN MY RUSH TO COMPLETE OUR QUICK TURN WITH A PAX WHO HAD ARRIVED EARLY I DID NOT PHYSICALLY REVIEW THE TEB 5 DEP PAGE. I HAD ASKED THE FO TO READ IT TO ME AND THEN I REPEATED IT BACK. UNFORTUNATELY; THE FO HAD NOT MENTIONED THE RESTRICTION OF NOT CLBING ABOVE 1500 FT TIL PASSING 4.5 DME FROM TEB. I HAD ALSO WRONGLY ASSUMED THAT I WAS FAMILIAR WITH ALL THE DEPS AND DID NOT NEED TO ACTUALLY SEE THE DEPARTURE PAGE.