GULFSTREAM GIV FLT CREW HAS A TRACK/HEADING AND ALT DEV DURING THE TEB 5 RWY 1 DEP.

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FLYING TEB 5 DEP FROM RWY 1 TEB CLBING THROUGH 1500 FT MSL STARTING THE TURN TO 040 DEGS; THE CO-PLT ENGAGED THE LNAV FROM HEADING (UNCOMMANDED) THIS GAVE ME A FULL R TURN COMMAND INSTEAD OF THE HEADING DIRECT TO PATTERSON PNJ NDB AS I EXPECTED. WHILE TRY TO DECIPHER THE COMMAND BARS I CONTINUED THROUGH THE ALT OF 2000 FT MSL -- THE DEP REQUIRES 2000 FT MSL TO BE MAINTAINED UNTIL CROSSING PNJ NDB. THE CO-PLT ENGAGED THE LNAV JUST AS WE WERE HANDED OFF TO DEP CTL AND CHKED IN ADVISING THAT WE WERE LEVELING AT 2000 FT MSL BUT WE WERE DRIFTING TO 2300 FT MSL. THE CTLR QUESTIONED OUR ALT AND ADVISED 'YOUR MODE C IS INCORRECT AND CONTINUE THE CLB TO AND MAINTAIN 6000 FT MSL DO NOT DSND BACK TO 2000 FT MSL.' NO CONFLICT WAS ENCOUNTERED. THE MOST CONTRIBUTING FACTOR TO THIS EVENT WAS THE CO-PLT ENGAGING THE LNAV GIVING ME COMMAND BARS THAT I DID NOT EXPECT. I SHOULD HAVE CLRED THE BARS AND FLOWN RAW DATA OR IF WE HAD TIME; ASKED FOR A DIRECT TO PNJ NDB TO LEVEL/SYNC THE BARS. THIS IS ULTIMATELY WHAT WAS DONE TO CORRECT THIS ERROR BUT WITH THE WORKLOAD AND TIME CONSTRAINT I WAS NOT ABLE TO REQUEST THIS ACTION. THE CREW NOW KNOWS THAT WE ONLY ENGAGE COMMAND INPUTS AS REQUESTED BY THE PLT FLYING AND DO NOT ATTEMPT TO FLY THE AIRPLANE FROM THE R SEAT.