FLC OF A FALCON FA20 OVERSHOT INTERMEDIATE CLB ALT DURING DEP CLB ACCORDING TO ARTCC CTLR.

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THE FLT DEPARTED FWA ON MAY/XA/00 AT APPROX XA50Z. INSTRUCTIONS WERE AS FOLLOWS: CLB TO 10000 FT AND TURN TO A HDG OF 050 DEGS TO JOIN THE CRUXX 4 ARR INTO YIP. ONCE WE WERE CLOSE TO REACHING 10000 FT WE WERE HANDED OFF TO ZAU ON THE FREQ OF 119.85 AND THE TIME WAS APPROX XC55Z. AT THIS TIME THE FO CHKED IN WITH CTR AND ASKED FOR HIGHER. ZAU CALLED OUT TFC AT THE 1 O'CLOCK POS AND THE FO IMMEDIATELY RESPONDED WITH 'TFC IN SIGHT.' THE CTLR THEN SAID TO THE OTHER ACFT THAT THE XING TFC HAS YOU IN SIGHT AND HE (THE CTLR) WAS GOING TO CLB US WITH VISUAL SEPARATION. THE NEXT BROADCAST ON THE FREQ WAS 'CLB TO FL210.' THE CAPT OF OUR FLT KEYED UP AND RESPONDED SAYING; 'ACR X IS CLBING TO FL210.' THE CAPT THEN INITIATED THE CLB TO FL210. AFTER WE WERE THROUGH AN ALT OF 12300 FT MSL; CTR CAME ON FREQ SAYING; 'ACR X WHAT IS YOUR ALT?!' THE CAPT RESPONDED BY SAYING; 'WE ARE CLBING TO FL210.' THE CTLR RESPONDED BY SAYING; 'I SAID 11000 FT AND NO HIGHER.' THE CAPT HAD ALREADY STARTED A DSCNT TO 11000 FT AND THE CTLR SAID; 'CLB TO AND MAINTAIN 17000 FT. AFTER ATC TOLD US 11000 FT AND NO HIGHER ANOTHER PLT CAME ON FREQ AND SAID; 'I HEARD IT TOO' MEANING HE HEARD THE CTLR TELL US TO CLB TO FL210. AT THIS POINT WE WERE HANDED OFF TO ZOB AND THE FLT CONTINUED AS PLANNED. DURING THIS WHOLE EVENT IT WAS AT LEAST FL200 AND CLR IN A 40 NM SURROUNDING AREA. THERE WAS NO CONFLICT WITH TFC SINCE WE HAD THE CLOSEST TFC IN SIGHT IMMEDIATELY. THE TIME WAS CLOSE TO IF NOT DURING CHICAGO'S MANY SCHEDULED ARRS. WX TO THE NE CLOSE TO CHICAGO INCLUDED RAINSHOWERS AND CONVECTIVE ACTIVITY. TREMENDOUS AMOUNT OF TFC AND BAD WX WERE THE MAJOR FACTORS IN THIS ALT CONFLICT.