A CL604 FO RPTS THE CAPT CLBED TO 2000 FT THEN DSNDED TO 1500 FT ON THE TEB 5 DEP. THE FO WAS SLOW IN HIS AFTER TKOF DUTIES DISTRACTING THE CAPT FROM LEVELING.

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AFTER CAREFUL REVIEW OF DEP ALTS; AFTER SETTING 1500 FT IN ASEL; WE BUSTED THE TEB DEP ALT (1500 FT) BY INADVERTENTLY GOING TO 2000 FT DEPARTING RWY 24. THE CAPT SELECTED VERT SPD COMMAND JUST AS THE FLT DIRECTOR SWITCHED TO ALT CAPTURE. HE THEN FOLLOWED VERTICAL SPD COMMANDS WHICH SHOWED A CONTINUED CLB. HE REALIZED HIS ERROR; BUT COULDN'T ARREST THE CLB UNTIL REACHING 2000 FT AND THEN DESCENDING. THE CAPT WAS DISTRACTED BY SLOWNESS OF COPLT IN SELECTING REQUESTED VERT MODES. I; THE COPLT; WAS SLOW IN SELECTING VERT MODES BECAUSE; ESPECIALLY AT NIGHT; I NEEDED TO SEARCH TO MAKE SURE I SELECTED THE CORRECT BUTTON IN ACFT I'M STILL GETTING USED TO. (ABOUT 6 MONTHS EXPERIENCE IN TYPE.) I AM ALSO SUPPOSED TO SPIN HEADING SELECTOR; RAISE FLAPS; AND REBUG SPD MODE; COMMUNICATE WITH DEP; AND SELECT CLB POWER SETTING ON FMS. I DROPPED THE BALL BY NOT PROPERLY MONITORING THE CAPT WHICH IS MY FIRST AND MOST IMPORTANT RESPONSIBILITY; ESPECIALLY DURING HIGH WORKLOADS. BOTH CREW ARE COMPLETELY FAMILIAR WITH THIS DEP. IT HAPPENS VERY QUICKLY. WE FAILED TO EXECUTE. FLY THE AIRPLANE FIRST. NAVIGATE THEN COMMUNICATE.