F100 FLT CREW EXPERIENCED ALT CLRNC CONFUSION WITH ZOB AND ZAU.

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WHILE IN CLB; FO GOT UP TO OPEN DOOR FOR MEALS. I WAS FLYING AND TEMPORARILY HANDLING RADIOS. ZAU RECLRED US FROM FL240 TO FL270; AND SAID FL290 WOULD BE FINAL FOR A WHILE AS TFC WAS PASSING OVERHEAD. I ADVISED FO OF FL290 FINAL. A SHORT WHILE LATER CTR RECLRED US TO FL330. FO RESPONDED WITH FL330 AND CTR DID NOT CORRECT; SO I COMMENTED THAT THE TFC MUST BE GONE. NEXT CTR CHANGED US OVER TO CLEVELAND AND SAID HIGHER WOULD BE AVAILABLE LATER. FO CHKED IN WITH 'OUT OF FL280 FOR FL330;' EMPHASIZING FL330. CTR RESPONDED 'ROGER.' AS WE CLBED THROUGH FL294; WE SAW TFC PASSING OVERHEAD AT FL310. I STARTED TO LEVELOFF; AND ATC ASKED IF WE WERE STOPPING AT FL390. FO RESPONDED THAT WE WERE PREVIOUSLY CLRED TO FL330 AND WE CHKED IN WITH CLB TO FL330. ATC RESPONDED THAT HE DID NOT HEAR IT; AS I DSNDED BACK TO FL290; AFTER REACHING A MAX OF FL295. CTR SAID HE WAS CHKING WITH CHICAGO AS THEY WERE ONLY SUPPOSED TO CLR US TO FL290; THEN GAVE US A FREQ CHANGE. PERHAPS I SHOULD HAVE BEEN A LITTLE MORE EMPHATIC ON VERIFYING THE ALT; BUT WE RESPONDED TO BOTH CHICAGO AND CLEVELAND WITH THE CLRNC TO FL330; WHICH WE ARE SURE CHICAGO GAVE US.