A BE-400 CREW INCORRECTLY SET THEIR ALTIMETERS TO INDICATE 1000 FT HIGH. WHILE CLIMBING ON THE TEB 5 THE AIRCRAFT WAS LEVELED AT 1800 FT; REALLY 800 FT; THEN A DESCENT WAS BEGUN TO 1500 FT WHICH WOULD REALLY BE 500 FT.

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ATIS ALTIMETER SETTING IS 29.53 FOLLOWING THE PASSAGE OF A WINTER STORM. CAPTAIN SETS THE STANDBY ALTIMETER TO 30.53 DURING PREFLIGHT CHECK BY INCREASING THE SETTING FROM THE 30.20 SETTING OF THREE DAYS PRIOR. UPON STARTUP; BOTH CREW MEMBERS SET THEIR EFIS ALTIMETER SETTINGS TO 30.53. NEITHER PILOT CORRECTLY READS THE ALTITUDE DISPLAYED DIGITALLY ON EFIS OR ANALOG DISPLAY ON STANDBY ALTIMETER. (CREW 'SEES' WHAT THEY EXPECT TO SEE.) NEITHER CREW MEMBER NOTICES THAT THE ALTITUDE ALERTER IS SET TO 3000 FT INSTEAD OF THE FIRST SID ALTITUDE RESTRICTION OF 1500 FT. CREW HAS BEEN FLYING TOGETHER FOR TWENTY YEARS AND HAVE NEVER HAD AN ALTITUDE BUST WHILE FLYING TOGETHER. CREW IS ASSIGNED THE TETERBORO FIVE DEPARTURE FROM RUNWAY 24 AND THE CAPTAIN LOADS THE DEPARTURE INTO THE FMS. SHORTLY AFTER DEPARTURE; FMS COMMANDS A TURN TO HEADING 280 BELIEVING THE AIRCRAFT HAS PASSED THE 1500 FT MSL AS STATED IN THE SID. CAPTAIN IS STARTLED BY THE SUDDEN COMMAND TO TURN BELIEVING THAT THE AIRCRAFT COULD NOT HAVE CLIMBED SO QUICKLY TO 1500 FT. CAPTAIN CHECKS ALTIMETER AND FOLLOWS FLIGHT DIRECTOR COMMAND TO TURN; BUT OVERSHOOTS THE 1500 FT LEVEL OFF BY 300 FT (ALTITUDE ALERTER INCORRECTLY SET TO 3000 FT; THANKFULLY IN THIS INSTANCE!). CAPTAIN BEGINS A SHALLOW DESCENT TO RETURN TO 1500 FT. DEPARTURE CONTROL ASKS CREW IF THEY ARE AT 800 FT. CREW BELIEVES THEY ARE AT 1800 FT AND DESCENDING TO THE SID MANDATED 1500 FT. EGPWS GOES OFF COMMANDING 'DON'T SINK.' CREW IS VERY CONFUSED BY THE CONFLICTING INFORMATION COMING FROM COCKPIT DISPLAYS; EGPWS CALLOUTS AND ATC. CAPTAIN THEN NOTICES THAT THE ALTIMETER SETTING IS 30.53 INSTEAD OF 29.53. CREW MAKES THE ALTIMETER CORRECTION AND CLIMBS TO THE CORRECT ALTITUDE. CREW WILL MAKE EVERY EFFORT IN THE FUTURE TO VERIFY THAT THE ALTITUDE DISPLAYED ON COCKPIT ALTIMETERS IS THE SAME AS FIELD ELEVATION FOLLOWING AN ALTIMETER SETTING CHANGE.