ACR X DEP MCI AND RESTR TO MAINTAIN 11000 FT BECAUSE OF AN INBOUND ACR Y DSNDING TO 12000 FT ON A HEAD-ON COURSE. THE CTLR INSTRUCTED THE INBOUND TO CONTINUE DSCNT AND MAINTAIN VISUAL SEPARATION FROM THE OUTBOUND AND THE OUTBOUND TO CLB; RPT SIGHTING THE DSNDING ARR. BOTH ACFT REQUIRED TURNS TO SAFELY PASS EACH OTHER.

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ACR X WAS CLBING ON THE LAKES 3 DEP FROM MCI. WE WERE CLRED TO CLB TO AN ALT OF 11000 FT AND RESTR AT THAT ALT DUE TO AN APCHING AIRLINER DSNDING TO 12000 FT. (I DON'T REMEMBER THE ACR BUT I BELIEVE IT WAS ACR Y). THE CTLR INQUIRED IF THE OTHER ACFT HAD OUR ACFT IN SIGHT AND HE REPLIED AFFIRMATIVELY. HE WAS SUBSEQUENTLY CLRED TO VISUALLY DSND BELOW 12000 FT AND TO KEEP VISUAL SEPARATION FROM OUR ACFT. WE WERE ASKED IF WE HAD THE OTHER ACFT IN SIGHT AND WE RESPONDED THAT WE DID NOT. WE WERE CLRED TO CLB TO A HIGHER ALT EVEN THOUGH WE HAD NO VISUAL CONTACT WITH THE OTHER ACFT. WE BEGAN A CLB AND WHEN WE FINALLY GOT VISUAL CONTACT WITH THE DSNDING ACFT; A R TURN WAS NECESSARY TO AVOID PASSING TOO CLOSE TO THE ACFT. HAD WE NOT TURNED WE WOULD HAVE PASSED AT A DISTANCE WHICH WAS NOT ACCEPTABLE AT MY COMFORT LEVEL. THE OTHER ACFT COMPLAINED TO THE CTLR THAT HE WAS NOT COMFORTABLE WITH THE SEPARATION AND IT APPEARED THAT HE DID NOT REALIZE HE HAD ACCEPTED A CLRNC TO DSND VISUALLY AND REMAIN CLR OF OUR ACFT. CORRECTIVE ACTIONS: IN A CASE WHERE 2 ACFT ARE APCHING EACH OTHER; I WOULD SUGGEST THAT BOTH ACFT HAVE VISUAL CONTACT BEFORE A CLRNC FOR A VISUAL CLB OR DSCNT IS ISSUED.