COMPLIANCE WITH A DME XING RESTR WAS MADE IN REF TO THE WRONG NAVAID; RESULTING IN AN ACR FLC DEV.

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I WAS THE FO AND THE CAPT WAS FLYING. WE WERE ON A FLT FROM CLEVELAND TO CHICAGO; MIDWAY. WE WERE WITH ZAU ON FREQ 135.90 AND HE TOLD US TO CROSS 20 MI W OF GOSHEN AT 10000 FT. I ACKNOWLEDGED; AND CAPT REPEATED TO ME '20 W OF GOSHEN AT 10.' I THEN SWITCHED TO MIDWAY ATIS ON #2 RADIO TO GET WX AND THEN CALLED IN RANGE TO COMPANY. I NOTICED THE CAPT WAS DSNDING. WHEN I CAME BACK ON #1 RADIO I SAW WE WERE AT ABOUT 13000 FT AND 18 MI W OF GOSHEN. I TOLD CAPT WE WERE TO BE AT 10000 FT 20 MI W OF GOSHEN THE LAST I KNEW; AND WE WOULDN'T MAKE IT. I ASKED IF THERE WAS A CHANGE WHEN I WAS OFF THE RADIO. HE SAID NO AND THAT HE COULD EASILY MAKE THE XING RESTR. I SAID 'NO WE ARE THERE NOW!' HE THEN NOTICED HE WAS LOOKING AT THE #2 DME WHICH WAS SET ON CHICAGO HEIGHTS AHEAD OF US INSTEAD OF THE #1 DME WHICH WAS SET ON GOSHEN; BEHIND US. HE PULLED THE SPD BRAKE AND PUSHED THE NOSE DOWN WHILE I GRABBED THE MIKE TO TELL CTR. CTR CALLED BEFORE I COULD GET A WORD IN AND TOLD US TO HURRY TO 10000 FT AND THAT WE HAD MISSED OUR RESTR. I RESPONDED AND BY THIS TIME WE WERE AT ABOUT 27 MI DME. ABOUT 20 SECONDS LATER WE WERE LEVEL AT 10000 FT AND I TOLD THE CTLR. THE CAPT WAS VERY ANGRY WITH HIMSELF FOR MISREADING THE DME AND I WAS VERY ANGRY WITH MYSELF FOR NOT CATCHING IT SOONER. (WHEN I SAW THE CAPT DSNDING SLOWLY; FOR A SECOND I THOUGHT THE CTLR MUST HAVE CHANGE THE RESTR WHEN I WAS OFF THE RADIO. BUT WHEN I QUESTIONED THE CAPT I REALIZED THAT WASN'T THE CASE). I WAS SO BUSY ATTENDING MY DUTIES GETTING THE WX AT CHICAGO THAT I GUESS IT IS IMPOSSIBLE TO DO EVERYTHING IN THE COCKPIT AND I JUST GOT OVERLOADED AND MISSED THE CAPT'S MISTAKE.