A LJ35 FLOWN BY A LOW TIME FO LEVELED AT 1800 FT ON THE TEB 5 DEP BEFORE DESCENDING TO 1500 FT THEN DRIFTING UP TO 2000 FT BEFORE THE 4.5 DME.

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DEVIATION OCCURRED ON THE TEB 5 DEP OFF OF RWY 24. THE DEP REQUIRES A CLB ON RWY HDG TO 1500 FT MSL. THEN TURN TO HDG 280 DEGS. AFTER REACHING 4.5 DME FROM TEB VOR; CONTINUE CLB TO 2000 FT MSL. MY FO; WHO WAS THE PLT FLYING; OVERSHOT THE INITIAL 1500 FT ALT BY 300 FT INITIALLY. I TOLD HIM TO GO BACK TO 1500 FT. HE DID THIS INITIALLY; BUT AS THE AIRSPEED INCREASED; HE DRIFTED BACK UP TO 2000 FT PRIOR TO THE 4.5 TEB VOR DME. ON INITIAL CONTACT WITH NY DEP; THE CTLR COMMENTED ON OUR PREMATURE CLB TO 2000 FT. HE THEN CLRED US UP TO 8000 FT. OUR ACFT WAS TCAS EQUIPPED; AND WE HAD NO CONFLICT WITH ANY OTHER ACFT. I HAD BEEN FLYING WITH THIS PARTICULAR FO FOR THE LAST COUPLE OF WEEKS. HE IS EXTREMELY LOW TIME WITH ONLY A FEW HRS IN LEAR JETS. I HAVE HAD TO TAKE CTL OF THE ACFT FROM HIM SEVERAL TIMES DURING THIS PERIOD. I TRIED TO TALK HIM THROUGH THE DEP WITHOUT HAVING TO TAKE THE ACFT FROM HIM AGAIN. OBVIOUSLY; THIS WAS A BAD IDEA. I SHOULD HAVE MADE THIS SOMEWHAT COMPLICATED DEP MYSELF AND GIVEN THE ACFT TO HIM AFTER WE WERE AT A SAFE SPEED AND ALT. ADDING TO THE COMPLEXITY OF THE DEP ITSELF WAS THE FACT THAT THE MAIN LNDG GEAR INBOARD GEAR DOORS 'THUMPED' SEVERAL TIMES BEFORE THEY FINALLY CLOSED.