FLT CREW OF C560 BUST THE 1500 FT MSL RESTR ON THE TEB DEP OFF RWY 24.

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DEPARTED RWY 24 AT TEB ON THE TEB 5 DEP; WHICH IS CLB TO 1500 FT; THEN R TURN TO 280 DEGS UNTIL PASSING TEB VOR 4.5 DME; THEN CLB TO 2000 FT; VERY SIMPLE. WELL; AFTER TKOF; WE WERE ACCELERATING VERY QUICKLY AND MY COPLT WAS BUSY ON THE RADIO (HE IS SOMEWHAT SLOW ON THE RADIO) TALKING TO TWR AND THEN SWITCHING TO DEP. AT 400 FT; HE DID NOT MAKE THE '400 FT' CALL AND I WAS WAITING FOR HIM TO FINISH SO HE COULD GET THE FLAPS UP. I ENDED PUTTING THEM UP AS WE WERE ACCELERATING THROUGH 190 KTS (200 KT SPD LIMIT FOR THE FLAPS). I HAD TO INCREASE THE RATE OF CLB SO AS NOT TO EXCEED 200 KTS AS I REDUCED PWR; BEFORE THE FLAPS FINISHED RETRACTING; THEN LEVEL OFF RIGHT AWAY AT 1500 FT. AT THIS POINT; I REDUCED PWR FURTHER AND STARTED THE TURN TO 280 DEGS WHILE ASKING THE COPLT IF WE COULD CLB TO 2000 FT. HE ANSWERED IN THE AFFIRMATIVE; SO I GRADUALLY CLBED TO 2000 FT. JUST BEFORE WE REACHED 2000 FT; THE DEP CTLR ADMONISHED US FOR BEING AT 2000 FT AND POINTED OUT TFC TO FURTHER EMPHASIZE HIS WORDS. I WAS BACK DOWN TO 1500 FT ALMOST BEFORE HE FINISHED AND EMBARRASSED. THERE WAS NO CONFLICT THOUGH. CONTRIBUTING FACTORS: 1) MY COPLT IS NEW TO JETS AND REALLY NEW TO THE ENCORE WHICH HAS EFIS/FMS AND ENOUGH PWR TO FLY LIKE A 'REAL' JET UNDER CERTAIN CONDITIONS. 2) MY COPLT; THOUGH A GOOD PLT; OPERATES IN 'SLOWER MOTION' THAN I AM USED TO AND I WAS EXPECTING HIM TO REMEMBER THIS OR AT LEAST LOOK IT UP ON THE PLATE. 3) I WAS FLUSTERED BY HAVING TO GET THE FLAPS UP; LEVEL OFF AT 1500 FT WHILE INCREASING THE RATE OF CLB AND TRYING TO KEEP THE FLT SMOOTH WHILE INITIATING A TURN AND FLYING AT 200 KIAS; SO I FORGOT THE POINT AT WHICH WE STARTED OUR CLB TO 2000 FT. 4) I WAS HAND FLYING. 5) WE HAD BRIEFED THE DEP TWICE WHILE NEGOTIATING TO GET A DEP SLOT AND THEN NEGOTIATING A FEW TFC JAMS ON THE GND AT TEB; THEN WE WERE CLRED FOR IMMEDIATE TKOF WHEN WE THOUGHT WE WERE #3 FOR DEP AND WERE NOT QUITE DONE WITH OUR 'BEFORE TKOF' CHKS. 6) I AM NEW TO BEING A CAPT; HAVING ONLY FLOWN COPLT AND THEN SINGLE PLT IN TURBOPROPS AND JETS AND AM STILL COMING UP TO SPD ON RUNNING A COCKPIT. I'M NOT TO THE POINT YET WHERE I CAN FLY BETTER THAN I USED TO BY MYSELF UNLESS I HAVE AN EXPERIENCED CO-CAPT/COPLT. 7) I ONLY HAD ABOUT 60 HRS IN THE ENCORE AND MOST OF IT AS A COPLT AT THE TIME OF THIS DEV; SO I AM NOT YET 100% CONVERSANT WITH THIS PLANE. IN THE FUTURE; I WILL BRIEF PROCS BETTER; FURTHER ENGAGE MYSELF IN THE COPLT'S ACTIVITIES; WHICH IS TO SAY; IMPROVE MY SITUATIONAL AWARENESS IN 2-PLT SITS; CONTINUE TO LEARN THIS PLANE (THE ENCORE) BETTER; WHICH I AM DOING WELL AT.