B190 CREW MISINTERPED ALT INSTRUCTIONS FROM ZKC RADAR CTLR AND DSND BELOW ASSIGNED ALT.

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ZKC INFORMED US TO 'EXPECT DIRECT KANSAS CITY AND CROSS 40 NM FROM KANSAS CITY AT 7000 FT.' HE THEN ADDED; 'GO DOWN TO 13000 FT FOR NOW.' WE BEGAN DSNDING FROM FL230. LATER; CTR SAID 'CLRED DIRECT KANSAS CITY.' THE CAPT AND I BOTH UNDERSTOOD THE XING RESTR TO STILL BE IN EFFECT AND INTERPED THIS CLRNC TO BE IN CONJUNCTION WITH THAT RESTR WHILE CONTINUING TO DSND. ATC ISSUED A TA '11:30 O'CLOCK POS; 12000 FT; OPPOSITE DIRECTION.' CAPT RESPONDED 'LOOKING FOR THE TFC.' NEITHER OF US COULD SEE THE TFC VISUALLY. FINALLY; ATC INQUIRED AS TO OUR ALT. CAPT READ BACK OUR INSTRUCTIONS TO CROSS 40 DME AT 7000 FT. ATC SAID WE WERE SUPPOSED TO REMAIN AT 13000 FT. HE THEN ADDED; 'TOO LATE NOW.' THE TFC THEN RPTED US 'IN SIGHT.' ONE REASON FOR THE OCCURRENCE WAS A CONFUSING CLRNC FROM ATC. THE OTHER REASON WAS A FAILURE TO VERIFY THE PROPER ALT BY BOTH THE FLT CREW AND ATC. IN THE FUTURE; I WILL INQUIRE ATC ABOUT DESIRED ALT UPON RECEIVING TA'S. SUPPLEMENTAL INFO FROM ACN 612065: AT 60 DME FROM MCI VOR WERE CLRED DIRECT MCI VOR. MYSELF AND THE FO INTERPED THIS CLRNC TO INCLUDE THE XING RESTR.