B737 FLC AND IAH LCL CTLR CHALLENGE EACH OTHER ON CORRECT ALT ASSIGNED ON GAR CAUSED BY INCORRECT SPACING BTWN LNDG AND DEPARTING TFC.

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WHILE ON SHORT FINAL APCH FOR LNDG ON RWY 26 AT IAH (1000 FT AGL); THE HOUSTON TWR CLRED ANOTHER COMPANY ACFT FROM THE RUN-UP BLOCK FOR AN IMMEDIATE TKOF ON RWY 26. AT 300 FT AGL THE TWR REALIZED THE CONFLICT WITH THE DEPARTING ACFT AND ORDERED MY FLT TO GO AROUND WITH NO MISSED APCH INSTRUCTIONS. WE INITIATED A STRAIGHT-OUT MISSED APCH AND AT 1000 FT MSL I ASKED THE TWR FOR MISSED APCH INSTRUCTIONS. THE TWR SAID 'TURN R HDG 060 DEGS AND CLB TO 3000 FT.' AT 2800 FT THE TWR SAID 'ACR X; I TOLD YOU TO CLB TO 2000 FT.' I SAID 'NO; YOU TOLD US 3000 FT.' THE TWR THEN SAID 'DSND TO 2000 FT.' I ACKNOWLEDGED THE CLRNC AND WE BEGAN A DSCNT TO 2000 FT. AT 2600 FT ANOTHER CTLR CAME ON AND SAID 'CLB TO 3000 FT.' WE THEN CLBED TO 3000 FT AND RETURNED FOR A NORMAL APCH AND LNDG. WHILE IN THE MIDDLE OF THE GAR; WE WERE ALMOST DIRECTLY ABOVE THE DEPARTING ACFT THAT WAS ALSO IN A R TURN TO 360 DEGS. AT THE TIME WE WERE AT 2800 FT AND THE CTLR SAID 'I TOLD YOU TO CLB TO 2000 FT;' WE WERE SEPARATED BY ONLY 900 FT ON THE TCASII. IF WE HAD LEVELED AT 2000 FT; WE WOULD HAVE COME EXTREMELY CLOSE TO AN NMAC WITH THE DEPARTING ACFT. BECAUSE OF THE CONFLICT THERE IS NO WAY WE COULD HAVE SAFELY LEVELED OFF AT 2000 FT. MISC DETAILS: SEVERAL DIFFERENT VOICES WERE COMING FROM THE TWR -- NOT JUST 1 CTLR. THE DEPARTING ACFT ON CLBOUT WAS ALSO EXPERIENCING MISCOMS WITH THE TWR.