MLG INADVERTENTLY DESCENDED THROUGH ASSIGNED ALT AND HAD LESS THAN STANDARD SEPARATION WITH SMT. ACFT WAS IN ROUGH IMC CONDITIONS.

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I WAS THE CAPT OF MLG X FLT FROM KC TO OKLAHOMA CITY. THE WX WAS IMC WITH CONTINUOUS LIGHT TO MODERATE TURB. WE BEGAN OUR DSCNT FROM FL310 TO FL240. THE F/A WAS IN THE COCKPIT AND I WAS TALKING TO FIRM. HE SAID THE PAX WERE READY TO GET ON THE GND BECAUSE OF THE ROUGH RIDE. WHILE WE WERE TALKING WE RECEIVED CLRNC TO CONTINUE OUR DSCNT TO 11000'. I WAS FLYING THE AIRPLANE AND THE F/O COPIED THE CLRNC. HE READ BACK 11000' (ACCORDING TO ATC TAPE); BUT SET 10000' IN THE ALT ALERT SYS. THE F/A LEFT THE COCKPIT AT ABOUT THAT TIME AND I MADE A PAX ANNOUNCEMENT TO THE PAX ABOUT THE WX AND ASKED THEM TO REMAIN SEATED FOR THE REMAINDER OF THE FLT. I REMEMBER BEING PLEASED THAT WE WERE ABLE TO CONTINUE OUR DSCNT UNRESTRICTED; BUT I DON'T REMEMBER WHETHER WE HAD BEEN CLRED TO 10000 OR 11000'. ALTHOUGH I HEARD THE CLRNC BEING GIVEN AND I HEARD MY F/O RESPOND. I DIDN'T HEAR THE SPECIFIC ALT. SUBSEQUENTLY; I LANDED THE ACFT AT 10000' AND THE CTLR AT KC CENTER ASKED US TO CONFIRM OUR ALT. THE F/O RESPONDED '10000.' THE CTLR THEN TOLD US THAT WE HAD BEEN CLRED TO 11000' AND TOLD US TO INCREASE OUR AIRSPD BUT TO STAY AT 10000'. I LATER WAS TOLD ON THE TELEPHONE BY A PERSON AT KC CENTER THAT WE HAD COME WITHIN 3.6 MI OF ANOTHER ACFT (I BELIEVE AN SMT); WHICH WAS ALSO AT 10000'. CONTRIBUTING FACTORS: WX--MY CONVERSATION WITH THE F/A AND MY PAX ANNOUNCEMENT TO THE PAX WAS BECAUSE OF THE ROUGH RIDE AND THE NEED TO REASSURE THEM THAT WE WOULD BE ON THE GND SOON AND THAT ALTHOUGH THE RIDE WAS UNPLEASANT; IT DIDN'T PRESENT ANY PARTICULAR PROB OR DANGER. I WAS ALSO CONCENTRATING ON FLYING THE AIRPLANE TO GIVE AS SMOOTH A RIDE AS POSSIBLE; MAINTAIN PWR CTL FOR ANTI ICING AND CONSTANTLY WATCHING THE RADAR TO AVOID TSTM CALLS. HABIT. WE ARE ALWAYS CLRED TO 10000' ON THE TRUMP 2 ARR; AND WHEN I SAW 10000' IN THE WINDOW IT DID NOT REGISTER AS A CONFLICT WITH ME. DISTR IN THE COCKPIT. TALKING TO THE F/A AND MAKING THE PAX ANNOUNCEMENT PRECLUDED ME FROM HEARING THE CLRNC IN ITS ENTIRETY. TIME DELAY. EVEN IF I HAD HEARD THE CLRNC TO 11000'; SINCE WE GOT THE CLRNC AT 25000-26000'; IT WAS NOT FRESH IN MY MIND AS WE LEVELED AT 10000'. WHEN THE CTLR SAW US DSNDING TOWARD ANOTHER ACFT; HE COULD HAVE REMINDED US THAT OUR CLRNC WAS TO 11000'. HE MADE NO ERROR; AS FAR AS I KNOW; BUT HE MIGHT HAVE PREVENTED WHAT COULD HAVE BEEN A FATAL ACCIDENT BY A SIMPLE REMINDER WHEN HE NOTICED THAT WE WERE DSNDING ON TOP OF ANOTHER ACFT.