A BE350 FLT CREW ON THE TEB DEP CLBED TO 2000 FT PRIOR TO TEB 4.5 DME; WAS ADVISED BY ATC TO DESCEND TO 1500 FT.

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THIS WAS THE 3RD LEG OF OUR TRIP. I HAD NOT LET THE CO-PLT FLY YET TODAY AND; WITH NO PAX ON BOARD I THOUGH SHE WAS UP TO THE TASK. THE TKOF WAS AT TEB; AND THE TEB 5 DEP. THERE WAS A STRONG; GUSTY CROSSWIND AND IT WAS ROUGH. OFF RWY 24 THE PROC IS CLB STRAIGHT AHEAD TO 1500 FT; TURN R TO 280 DEGS; THEN AT 4.5 DME FROM TEB CLB TO 2000 FT. I THOUGHT THINGS WERE GOING WELL; EVEN THOUGH SHE REALLY HAD HER HANDS FULL OF AIRPLANE; UNTIL ALL OF A SUDDEN WE WERE AT 2000 FT. (THE 350 CLBS MUCH BETTER THAN THE 90 SHE IS USED TO FLYING.) BEFORE WE HAD TIME TO FIX IT; THE TWR WAS TELLING US TO GO BACK TO 1500 FT NOW. SHE REDUCED THE PWR A LITTLE. I REDUCED THE PWR A LOT. ONCE AT 1500 FT SHE WAS HAVING TROUBLE MAINTAINING ALT IN THE TURB AND CHANGING PWR SETTINGS. AS I WAS TRYING TO CHK ON WITH APCH; ON THE WRONG FREQUENCY (I REALLY DON'T KNOW HOW I MESSED UP; WE HAD PLENTY OF TIME ON THE GND AND I SET IT UP BEFORE WE TOOK OFF); WE FLEW THROUGH THE TEB 4.5 DME WITHOUT CLBING UP TO 2000 FT. AFTER CHKING WITH THE TWR FOR THE CORRECT FREQUENCY AND GETTING TO APCH THEY COMMENCED TO EDUCATE US ON THE PROPER WAY TO EXECUTE THE DEP. I'VE DONE THIS DEP MANY TIMES; BUT THERE WAS NO WAY THEY COULD TELL THAT TODAY. FROM THAT POINT ON; ALL WAS WELL. EVEN THOUGH IT MIGHT NOT HAVE BEEN OBVIOUS; WE DID BRIEF THE DEP; MORE THAN ONCE; BUT THINGS DID NOT GO AS BRIEFED. EVEN THOUGH WE WERE WELL RESTED; FATIGUE MAY HAVE BEEN A FACTOR. THE PREVIOUS LEG HAD BEEN CHALLENGING (WE HAD TO HOLD AT THREE DIFFERENT PLACES) AND IT WAS TURBULENT. MAINLY; I SHOULD HAVE BEEN FLYING THE AIRPLANE. TEB IS CHALLENGING ENOUGH FOR ANY PLT UNDER ANY CIRCUMSTANCES. HER WITH LESS THAN 1000 HRS TOTAL TIME AND LOW TIME IN AN AIRPLANE THAT SIZE AND ME TRYING TO MONITOR THAT AND DO MY DUTIES UNDER THOSE CONDITIONS AND IN THAT HIGH DENSITY ENVIRONMENT WAS JUST TOO MUCH. I SHALL BE DEDICATED TO USE BETTER JUDGEMENT IN THE FUTURE.