AN LJ-31 DEPARTING TEB ON THE DALTON DEP FAILED TO LEVEL AT THE CHARTED ALT AND EXPERIENCED A TCAS ALERT REQUIRING EVASIVE ACTION.

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TEB 19 DALTON DEP LJ-31 PART 91 CREW ONLY REPOSITIONING FLT. NIGHT VFR. ON THE DALTON DEP FROM RWY 19 AT TEB; WE FAILED TO LEVEL OFF AT 1300 FT. AT APPROX 1800 FT I WAS IN THE R SEAT ATTEMPTING TO CONTACT NEW YORK DEP WHEN I NOTICED AN AIRLINER AT OUR 12 O'CLOCK POS. I TOOK CTL; INITIATED A DSCNT AND TURNED R TO APPROX 320 DEGS FOR SPACING. NEW YORK DEP INFORMED US WE WERE SUPPOSED TO BE AT 1300 FT AND THAT THE AIRLINER HAD ALSO DEVIATED TO AVOID US. OUR TCAS ISSUED AN AUDIBLE TFC ALERT AS WE PASSED BEHIND AND BELOW THE AIRLINER. THE DEP PROC WAS IMPROPERLY BRIEFED AND THE PNF DID NOT CALL FOR LEVELOFF AT 1300 FT AND VERIFY THE AIRPLANE HAD STOPPED CLBING. THE PF BRIEFED ME THAT CLRNC HAD CHANGED US FROM THE TEB 5 TO THE DALTON VFR DEP AND THE ALT WAS 4000 FT. THE PF COPIED BOTH ATIS AND THE CLRNC. ALT PRESELECT WAS SET BY PF TO 4000 FT. FAILURE OF THE PNF TO LISTEN TO THE ATIS; WHICH LATER THIS DAY INCLUDED 'PLTS MUST STRICTLY ADHERE TO PUBLISHED ALT RESTRS' AND FAILURE OF PNF TO BE LISTENING TO THE CLRNC GIVEN CONTRIBUTED. TEB TWR CLRED US FOR TKOF WHILE STILL ON TXWY P. THERE WAS SIGNIFICANT TAXI TIME BTWN CLRNC AND ACTUAL TKOF. THIS EARLY TKOF CLRNC MAY HAVE CONTRIBUTED TO A QUICK TKOF BRIEFING WHICH ONLY INCLUDED INITIAL ALT 800 FT AND HDG OF 280 DEGS RATHER THAN THE FULL DEP PROC WITH 1300 FT LEVELOFF AND EFC AFTER XING TEB 230 DEGS. HAD TEB TWR ALSO NOTIFIED US OF TFC; THAT MIGHT HAVE HELPED. WE SCREWED UP BIG! BLEW THE ALT. PNF RELIED ON THE PF'S UNDERSTANDING OF THE SID AND DEP CLRNC WITHOUT CONFIRMING THE DEP PROC PRIOR TO TKOF. PNF FAILED TO MONITOR ALT AND REMIND AND INSIST ON LEVELOFF AT 1300 FT. FAILURE OF BOTH PLTS TO VERIFY CLRNC; WHETHER OR NOT A DEV FROM THE STANDARD PROCS WAS AUTH. CONTRIBUTING: PF IS THE WEAKER OF THE 2 PLTS; EARLY MORNING DEP; AND APPARENT LACK OF TFC MAY HAVE LED TO COMPLACENCY. STRONG RELIANCE OF PF ON PNF FOR DIRECTION. FAILURE OF PNF TO RECOGNIZE DEV IN ALT. NO MENTION IS MADE ON CHARTS OF ARPT OR ATIS THAT THE FLOOR OF THE CLASS B AIRSPACE OVERLYING TEB IS 1800 FT. AT OTHER ARPTS UNDERLYING CLASS B AIRSPACE; THE FLOOR IS DESCRIBED ON ATIS.