CITATION CE560XL FLT CREW HAS AN ALT EXCURSION DURING THE TEB 5 DEP.

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I WAS FLYING AS COPLT (PNF) IN OUR COMPANY ACFT. WE DEPARTED TEB ON THE TEB 5 DEP SID. WE WERE CLBING OUT ON RWY HEADING (AS DEPICTED ON CHART) TO 1500 FT MSL. AS WE REACHED 1500 FT; WE TURNED TO 280 DEG HEADING. THE CAPT AT THAT TIME REACHED OVER AND TURNED THE ALT ALERTER UP THINKING IT WAS TIME TO CLB HIGHER. AT THAT POINT WE WERE HANDED OVER TO NY CTR AND I MISTAKENLY READ BACK CLBING TO 2000 FT MSL. THE CTLR SAID IT SHOULD BE 1500 FT; AND I REPLIED ROGER 1500 FT. THE DEP REQUIRES 2000 FT AFTER 4.5 DME FROM TEB VOR. I THINK WE WERE ABOUT 4 DME. THE CAPT WAS HAND FLYING THE ACFT AND WHEN HE SPUN THE ALT ALERT HE CLBED TO I THINK 1700 FT TO 1800 FT. I KNOW WE NEVER REACHED 2000 FT AND WE HAD NOT RECEIVED A TCAS ALERT. CAPT RETURNED TO 1500 FT. I HAVE FLOWN THAT DEP SID AT TEB SEVERAL TIMES AND THE SID WAS BRIEFED WELL BEFORE TAKEOFF. I HAD SET UP THE FMS WITH THE SID AND I'M NOT SURE WHY THE CAPT WAS HAND FLYING. I THINK IN THE CONFUSION OF THE CAPT SPINNING THE ALT ALERTER THINKING IT WAS TIME TO CLB AND NOT BEING AT 4.5 DME HE FLEW THROUGH THE 1500 FT ALT. LOOKING BACK I THINK WE BRIEFED THE SID PROPERLY. I THINK THE AUTOPLT SHOULD HAVE BEEN USED TO HELP ON A COMPLICATED SID. HAD THE CAPT NOT TURNED ALT ALERTER PREMATURELY I WOULD HAVE CALLED CLBING TO 2000 FT. I THINK NOT USING THE AUTOPLT AND THE CAPT THINKING IT WAS TIME CLB AT THE TURN TO 280 DEGS NOT AT 4.5 DME WERE FACTORS. SUPPLEMENTAL INFO FROM ACN 706894: AFTER DEPARTING RWY 24 FROM TEB ARPT; MY FO WAS INSTRUCTED TO CONTACT NY DEP CTL. AT THAT SAME TIME I HAD LEVELED AT 1500 FT MSL AND STARTED THE R TURN TO 280 DEGS IN ACCORDANCE WITH THE TEB 5 DEP. THE FO'S FIRST COMMENT TO NY DEP WAS THAT WE WERE CLBING TO 2000 FT. THIS CALL WAS IN ERROR BECAUSE WE HAD NOT YET PASSED THE 4.5 DME TEB FIX. THIS CONFUSION WAS RESOLVED AND WE CONTINUED THE FLT TO OUR DEST.