ACR MLG REPORTED ALT DEVIATION CLRNC DISPUTED.

Narrative

FLYING AT FL310 (FILED ALT) FROM AUSTIN TO MIDLAND ON THE SJT 102 DEG R INBND 80 MI OUT. REQUESTED FL350 FROM ZHU. ZHU CLRED US TO CLB AND MAINTAIN FL350. I USED THE FULL CALL SIGN ON READBACK AND SAID WE WERE LEAVING FL310 FOR FL350. THE F/O FLYING ALSO HEARD THE PROPER CALL SIGN AND CLRNC FROM ZHU (132.72). PASSING THROUGH FL330 CENTER CALLED AND ASKED FOR OUT ALT. I ADVISED WE WERE PASSING FL330 FOR FL350. ZHU AT THAT TIME SAID OUR ASSIGNED ALT WAS FL310. I REPLIED THAT WE REQUESTED FL350 AND THAT WE HAD BEEN CLRED TO CLB TO THAT ALT. I THEN ASKED WHAT THEY WOULD LIKE FOR US TO DO. CENTER SAID TO CLB AND MAINTAIN FL350. I REPLIED TO CLB AND MAINTAIN FL350 AS PREVIOUSLY CLRED. I FEEL THE REASON FOR THE MISUNDERSTANDING WITH ZHU WAS BROUGHT BY THE FACT THAT THIS CTLR WAS WORKING MORE THAN 1 CENTER FREQ. EVEN THOUGH OUR FREQ (132.72) WAS NOT THAT CONGESTED; THE OTHER FREQ APPEARED TO BE BECAUSE WE COULD HEAR THE CTLR COMMUNICATING CONSTANTLY WITH ACFT BUT WITH VERY LITTLE RESPONSE FROM THEM ON OUR FREQ. I HAVE ALWAYS FELT THAT THIS IS AN UNSAFE SITUATION WHEN A CTLR DOUBLES UP ON APCH OR CENTER FREQS. NOT ALL CTLRS ARE CAPABLE OF HANDLING THIS TYPE OF SITUATION WHICH IS OBVIOUS WITH OUR OCCURRENCE THAT WE JUST EXPERIENCED.