B737 FO RECEIVES AND ACKNOWLEDGES CHANGE OF RTE CLRNC FROM I90 WHILE CAPT IS ON COMPANY FREQ. I90 ISSUES CORRECTIVE HDG CHANGE WHEN NOT OBSERVING COURSE CHANGE AT DRXLR INTXN.

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ON ARR TO HOU; PASSING ABOUT 14000 FT TO 10000 FT; I (THE CAPT) WENT OFF ATC FREQ TO CALL COMPANY IN-RANGE FOR THE GATE. WE WERE ON THE ROKIT 2 ARR. HOU APCH INSTRUCTED US TO FLY 300 DEG HDG OUT OF DRXLR INTXN; THEN CHANGED IT TO 290 DEG HDG. MY FO ACKNOWLEDGED THE HDGS AND IMMEDIATELY TURNED TO 300 DEG HDG AND THEN 290 DEG HDG; BUT DID NOT HEAR OR REPEAT OUT OF DRXLR. MEANWHILE; I CAME BACK TO ATC FREQ. ABOUT 1 MIN LATER; HOU APCH SAID 'TURN L IMMEDIATELY TO 180 DEG HDG AND REJOIN THE APCH.' HE ADDED THAT THE 290 DEG HDG WAS OUT OF DRXLR. I CALLED HOU APCH ON THE GND VIA LANDLINE AND LISTENED TO THE TAPES. THE PROBS I SEE ARE TWO: 1) HOU APCH ALWAYS ASSUMES A LCL HOU AIR CREW WHO ARE USED TO LCL PROCS AND PROCEEDS AT LIGHTNING SPD WITH SOMETIMES ABBREVIATED ACKNOWLEDGEMENTS FROM US. 2) WE ARE ALWAYS AT RISK WHEN ONE CREW MEMBER GOES OFF FREQ TO COMPANY AND AT THAT MOMENT; WE ARE NOT BACKING EACH OTHER UP. IN THE FUTURE; I'LL BE MORE CAREFUL WHEN I GO OFF APCH FREQ. MAYBE WE SHOULD CALL IN-RANGE ABOUT FL180; BEFORE THINGS GET BUSY WITH APCH. THIS WAS ONLY MY FO'S THIRD ARR IN HOU AIRSPACE AND I SHOULD HAVE BEEN MORE ATTENTIVE.