AN E145 CREW; DEPARTING IND; MISINTERPED A CLRNC AND OVERSHOT ASSIGNED ALT.

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ON DEC/MON/01 THE CAPT AND I BEGAN OUR DAY AT XA45. WE DEPARTED FOR A ROUND TRIP FLT FROM CLE TO IND. THIS FLT WAS THE FIRST TIME THE CAPT AND I HAD FLOWN TOGETHER. HOWEVER; I FELT THAT WE WERE VERY STANDARD IN OUR PROCS (AS WE ARE TRAINED) AND WAS COMFORTABLE WORKING AS A CREW. ON THIS DAY; THE WX WAS ADVERSE IN EVERY WAY. SHORTLY AFTER TKOF; WE WERE IMC AND REMAINED IN THOSE CONDITIONS UNTIL THE FINAL APCH SEGMENT; NEARLY DOWN TO MINIMUMS. WE ENCOUNTERED IN OUR FIRST LEG (ENRTE TO IND) ICING; RAIN; LIGHT CHOP AND MODERATE TURB. OTHER THAN THE WX CONDITIONS; HOWEVER; THE FLT WENT VERY WELL. THE VISIBILITY IN INDIANAPOLIS DURING OUR ARR WAS ABOUT 1 1/2 MI; BUT THE TWR REQUESTED VISUAL CONFIRMATION OF OUR LNDG FROM AN ACR HOLDING SHORT OF RWY 5R (WHERE WE WERE CLRED TO LAND). IT WAS A BAD WX DAY. WE PERFORMED A QUICK TURN IN INDIANAPOLIS (20 MINS) AND BEGAN OUR TAXI BACK TO RWY 5R. AFTER COMPLETING THE TAXI AND BEFORE TKOF CHKLISTS; WE TAXIED INTO POS AND HOLD ON RWY 5R AFTER AN ACR B737 BEGAN HIS TKOF ROLL. WE WERE CLRED FOR TKOF AND RECEIVED OUR CLRNC AS PREVIOUSLY GIVEN TO CLB AND MAINTAIN 5000 FT. THE TWR HANDED US OFF TO DEP WHO THEN GAVE US OUR NEW ASSIGNMENT. APPARENTLY; HE CLRED US TO 6000 FT AND A HDG OF 070 DEGS. THE CONFUSION CAME IMMEDIATELY AFTER OUR READBACK WHEN ANOTHER ACFT ON THE ARR INTO IND WAS CLRED TO DSND TO 7000 FT. THE CTLR READ THE CLRNC TO THE DSNDING ACFT WHILE THE CAPT WAS DIALING IN OUR ASSIGNED ALT AND CAUSED US TO MAKE THE MISTAKE FROM WHAT I CAN GATHER. THE CAPT DIALED IN 7000 FT INSTEAD OF 6000 FT. HE CALLED OUT LIKE ALWAYS '7000 FT SET' AND I; THINKING HE WAS CORRECT; JUST REPLIED '7000 FT SET' WITHOUT ALARMING MYSELF. ONCE WE REACHED 6500 FT; I REALIZED THAT SOMETHING WASN'T RIGHT AND STARTED TO SHALLOW MY CLB RATE. SIMULTANEOUSLY; WE RECEIVED A MASTER CAUTION FOR TFC 'TA' ONLY FOR THE DSNDING ACFT. HE WAS STILL 3-4 MI AWAY AND 1500-1700 FT ABOVE US. ATC PIPED IN AND ASKED US IF WE WERE AT 6000 FT AND THEN WE BEGAN DISCUSSING AND TRYING TO CLARIFY WHAT OUR ASSIGNED ALT HAD BEEN. ATC LEVELED THE OTHER ACFT AT 8000 FT FOR SAFETY AND I IMMEDIATELY WENT BACK TO 6000 FT. THE TA WENT AWAY WITHIN 5 SECONDS AND BOTH PARTIES CROSSED AREAS BY 2000 FT AND SEVERAL MI APART. WE WERE ASKED TO CONTACT ZID ON THE GND; SO WE DID. SUPPOSEDLY; THEY DISMISSED EVERYTHING WHEN THE CAPT SAID IT WAS A CLARIFICATION PROB; BUT I FELT THIS SHOULD BE MADE KNOWN FOR SAFETY PURPOSES. I BELIEVE THE PROB CAME UP BECAUSE OF SIMILAR CLRNCS. WE HAD 070 DEG HDG AND 6000 FT. THE OTHER ACFT RECEIVED 7000 FT. THE NUMBERS WERE CLOSE AND SOMEHOW WE MADE THE MISTAKE EVEN WITH 2 OF US. POSSIBLE EXTERNAL DISTRS OCCURRED DUE TO EARLY MORNING START; NEW CREW WORKING TOGETHER; WX FATIGUE FACTORS; BAD TIMING; ETC. I BASICALLY LEARNED THAT SITUATIONAL AWARENESS CANNOT BE DISCOUNTED REGARDLESS OF ANY CIRCUMSTANCES. OBVIOUSLY; SAFETY COULD HAVE BEEN COMPROMISED; AND I'M GRATEFUL IT WASN'T BUT IT WAS AN HONEST MISTAKE AND I THINK ATC AND BOTH CREWS WERE ASSERTIVE IN CORRECTING THE PROB.