FLC OF A DASSAULT FALCON DA20; OVERSHOT CLB ALT DUE TO A MISUNDERSTANDING OF ATC CLRNC.

Narrative

ON THE MORNING OF JUN/XA/97 WE DEPARTED IN LTT FROM UGN TO BJS. MY COPLT WAS FLYING ON THE L SIDE. MY COPLT IS ALSO PIC QUALIFIED IN DA20 ACFT. ON CLBOUT FROM 3000 FT WE CLBED TO 5000 FT. I SET 5000 IN THE CTL WINDOW AND CONFIRMED IT WITH MY COPLT BY STATING CLB TO 5000 FT. WE WERE LEVEL AT 3000 FT AND I THOUGHT THAT ATC STATED; 'LTT CLB AND MAINTAIN 5000 FT.' AFTER LEVELING AT 5000 FT; OUR CHICAGO DEP CTLR ASKED US WHAT ALT WE WERE CLBING TO. I STATED 5000 FT IS WHAT WE WERE CLRED TO. THE CTLR STATED 4000 FT WAS THE ALT WE WERE CLRED TO AND THEN STATED 5000 FT. I EXPRESSED MY CONCERN TO THE CTLR AND TOLD HIM I WAS SORRY AND THOUGHT 5000 FT WAS THE ALT. I BELIEVE THAT IT IS POSSIBLE THAT THE CTLR DID STATE 4000 FT. HOWEVER; MY CREW AND I THOUGHT 5000 FT. IF IT IS POSSIBLE THAT THE CTLR DID STATE 4000 FT; I FEEL THAT DUE TO OUR BUSY SCHEDULE ON THE INITIAL CLB PHASE; IT IS POSSIBLE WE MAY HAVE SET THE WRONG ALT IN THE CTL WINDOW. IT WAS EARLY IN THE MORNING AND THE CREW MAY NOT HAVE BEEN AS SHARP AS THEY SHOULD BE. I THOUGHT THAT BY CONFIRMING BTWN THE CREW THE ALT CLRED TO CLB IS A GOOD PROC TO FLT ALT.