RWY INCURSION AND CRITICAL GND CONFLICT OCCURS AT THE JUNCTION ON RWY 22 AND RWY 32L WHEN A STUDENT PLT AND CFI MISINTERP THEIR MISSED APCH CLRNC FOR A LNDG CLRNC DURING ILS APCH TO RWY 32L AT CMI; IL.

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MY STUDENT AND I EXPERIENCED A RWY INCURSION THROUGH THE 32L/22R INTERSECTION AT CMI. WE WERE FLYING THE ILS 32 PRACTICE APCH AND DID A TOUCH-N-GO THROUGH THE INTERSECTION WHILE ANOTHER ACFT; ACFT Y WAS CLRED FOR A TOUCH-N-GO ON THE INTERSECTING RWY 22R. AS A RESULT; WE BOTH PASSED THROUGH THE INTERSECTION AT THE SAME TIME; WITH MY PLANE PASSING 300FT OVERHEAD. AFTER TALKING WITH THE TWR AFTER THE INCIDENT; WE DETERMINED THAT MISCOMMUNICATION AND CONFUSION WAS AT FAULT. ON OUR APCH; INSIDE THE FINAL APCH FIX; WE WERE ASKED IF WE WANTED A TOUCH-N-GO OUT OF OUR APCH AND WE REPLIED 'AFFIRMATIVE.' TWR THE STATED; 'CLR TO LAND RWY 32; HOLD SHORT RWY 22 AND WAIT FOR RELEASE.' WE FULLY READBACK THE CLRNC. APPROX 20 SECS LATER TWR THEN STATED; 'ACFT X; CONTINUE MISSED APCH; MAINTAIN 3000 FT TURN R 90 DEGS TO INTERCEPT THE 60 DEG RADIAL;' TO HOLD AT A FIX. THROUGH PAST EXPERIENCE; I INTERPRETED THIS CLRNC AS A TOUCH-N-GO AND AFTER THAT WE WERE CLRED TO THE HOLDING FIX. THIS HOWEVER; WAS NOT WHAT TWR WANTED US TO DO AS THEY WERE EXPECTING US TO LAND; HOLD SHORT; AND THEN AWAIT A RELEASE. TO PREVENT AN INCIDENT LIKE THIS FROM HAPPENING; I SHOULD HAVE QUERIED ATC ABOUT THE CLRNC INSTEAD OF ASSUMING WE WERE CLRED FOR THE TOUCH-N-GO. IN ADDITION I SHOULD HAVE BEEN MORE AWARE OF THE SURROUNDING TFC THAT WAS PRACTICING LNDGS ON THE INTERSECTING RWY. ALSO; ATC SHOULD HAVE BEEN MORE SPECIFIC IN THEIR CLRNC AND NOT GIVEN ANY MISSED APCH INSTRUCTIONS UNTIL WE WERE STOPPED ON THE RWY AND CLRED FOR TAKEOFF.