ACR FLC ARE ASSIGNED MULTIPLE DEP HDGS PRIOR AND ON DEP ROLL WITH AN ALT CHANGE. MKE TRACON CHALLENGES ALT ASSIGNMENT.

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ON MKE DEP FREQ 125.35 AT APPROX XA21Z; VECTORS WERE GIVEN WITH INITIAL DEP CLRNC OF 5000 FT. ON RWY; A DEP HDG WAS ASSIGNED 210 DEGS. ON DEP; A HDG OF 250 DEGS WAS ASSIGNED. THE CTLR THEN ASKED; 'ACR X WHERE ARE YOU GOING TODAY -- PHX?' PNF REPLIED; 'AFFIRMATIVE' AND THE CTLR ASSIGNED A 270 DEG HDG WITH 7000 FT ALT ASSIGNED. AS WE PASSED THROUGH APPROX 6700 FT; THE CTLR REPLIED; 'TURN TO A 290 DEG HDG AND YOU WERE ASSIGNED 5000 FT.' THE ALT WAS CONFIRMED AS 7000 FT BY BOTH PLTS. AT NO TIME IN THE COCKPIT WAS THERE A QUESTION OF WHAT WAS ASSIGNED AND WE THEREFORE QUESTIONED THE CTLR. THE CTLR ASSIGNED A 270 DEG HDG AND INSISTED HE WAS CORRECT. SUPPLEMENTAL INFO FROM ACN 439779: PASSING THROUGH 6700 FT; CTLR SAID TO 'TURN TO HDG 290 DEGS; YOU WERE CLRED TO 5000 FT.' I RESPONDED; 'SIR; YOU HAVE US 7000 FT.' HE SAID; 'NO; YOU WERE ASSIGNED 5000 FT; TURN HDG 270 DEGS.' END OF DISCUSSION! CREW WAS AWARE OF ALT ASSIGNED AT ALL TIMES. WE VEHEMENTLY AGREE ON THIS MATTER. NO DEV ON OUR PART. HEARBACK/READBACK DISAGREEMENT. PLT/CTLR MULTIPLE CLRNCS.