MDT CREW FLYING A MODIFIED SID DEPARTED ASSIGNED ALT AT THE DME FIX INSTEAD OF AT ATC'S REQUEST.

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DEPARTED RWY 24 AT TEB. CLRNC WAS TO FLY TEB 4 DEP. PROC CALLS FOR CLB TO 1500 FT MSL UNTIL PASSING 4.5 DME AND CONTINUE CLB TO 3000 FT MSL. CREW BRIEFED EACH OTHER ON DEP BEFORE TKOF. AFTER TKOF; NEW YORK DEP CALLED TFC AND INSTRUCTED CREW TO FLY AND MAINTAIN 1500 FT MSL IN ACCORDANCE WITH THE SID. THE CREW READ BACK TO MAINTAIN 1500 FT AGL IN ACCORDANCE WITH THE DEP. AT 4.5 DME CREW STARTED SLOW CLB TO 3000 FT MSL. NEW YORK DEP INSTRUCTED US THAT WE WERE FLYING A FUNNY LOOKING 1500 FT MSL. CREW STATED THAT WE WERE GIVEN CLRNC TO FLY IN ACCORDANCE WITH THE SID. ATC DISAGREED; STATING WE WERE CLRED TO MAINTAIN 1500 FT MSL AND FLY THE DEP. NOTICEABLY ABSENT WAS THE TERM 'IN ACCORDANCE.' NEW YORK DEP STATED; IT DIDN'T MATTER AND ISSUED A CLRNC TO HIGHER ALT. THERE WAS NO KNOWN TFC CONFLICT TO THE FLC. I FEEL CONTRIBUTED FACTORS WERE. RADIO CONGESTION; DENSE TFC; AND NONSTANDARD PHRASEOLOGY. THE CREW HAS FLOWN TO TEB FOR OVER 20 YRS AND HAS NEVER BEEN INSTRUCTED TO 'FLY AN ALT IN ACCORDANCE WITH THE SID.' WE SHOULD HAVE QUESTIONED CLRNC.