MD80 FLC INBOUND TO IAH ON 12 MI FINAL NOTICED TFC ON TCASII ABOVE THEIR ACFT. THE PLT TURNED L TO AVOID THE TFC AND LATER WAS TOLD THE OTHER ACFT WAS LINED UP ON THE WRONG PARALLEL RWY.

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ON GS AT APPROX 2500 FT; RWY 27 ILS IAH NOTICED TARGET SUPERIMPOSED US ON TCASII SCREEN SHOWING 1000 FT ABOVE. TCASII DISPLAY TARGET WAS SUPERIMPOSED SO THAT THE READOUT WASN'T LEGIBLE. WE BROKE OFF APCH TO S AND ASKED TWR IF THERE WAS AN ACFT ABOVE US; THE CTLR COMMANDED A L TURN HDG 180 DEGS. NO TCASII WARNINGS OR ALERTS WERE DISPLAYED OR RECEIVED AT ANY TIME. THE TARGET WAS A CHALLENGER BUSINESS JET ON WRONG PARALLEL RWY APCH. ADDITIONALLY; THE TWR FINAL MONITOR DID NOT PICK UP THE CONFLICT. WE BELIEVE CONFLICT WAS WITHIN 300 FT VERT; ZERO FT HORIZ. THE CPR JETS NEED TCASII. SUPPLEMENTAL INFO FROM ACN 411733: AN ACFT WAS NOTICED ON THE TCASII SCREEN DIRECTLY OVERHEAD AT 700 FT AND DSNDING. THE CHALLENGER JET ABOVE DID NOT RECEIVE ANY ALERTS BECAUSE OF NO TCASII INSTALLATION. THE CHALLENGER WAS SUPPOSED TO BE LINED UP FOR RWY 26; IS WHAT WE WERE TOLD BY THE TRACON SUPVR. THERE WAS ALSO TRAINING GOING ON AT THE TIME. IT IS MY FEELING THAT A CTLR MISTAKE WAS MADE AS THIS ACFT WAS DIRECTLY OVERHEAD AND DSNDING UNKNOWING THAT WE WERE THERE TO A DISTANCE OF 300 FT VERTLY. WHY NO ONE BUT US NOTICED THIS I DON'T KNOW.