AIR TAXI PLT LEAVES ALT WITHOUT CLRNC WHEN ONE WAS EXPECTED.

Narrative

WE WERE ON AN IFR FLT PLAN BTWN LOUISVILLE; KY; AND WAUKESHA; WI. THOUGH WE HAD REQUESTED AND BEEN GIVEN AN EXPECTED CRUISE ALT OF FL390; UPON REACHING FL290 WE WERE INFORMED THAT FL290 WOULD BE OUR FINAL CRUISE ALT TO OUR DEST. I IN TURN ACKNOWLEDGED HIS XMISSION. SUBSEQUENTLY THE CAPT ASKED THE CTR CTLR FOR ANY OPTIONS TO TAKE US HIGHER. AT ONE POINT IN THEIR DIALOGUE THE CTLR STATED 'IF YOU CAN COME L TO 300 DEGS; I CAN GIVE YOU FL310.' SIMULTANEOUSLY; I WAS OCCUPIED ON THE #2 COM TRYING TO RECEIVE THE AWOS FOR WAUKESHA. WHEN I TURNED MY ATTN BACK TO THE CAPT; A FEW MOMENTS LATER; HE STATED; WE ARE 300 DEGS ASSIGNED AND FL310. WE IN TURN DEPARTED FL290 FOR FL310. WITHIN A FEW SECONDS THE CTR CTLR REQUESTED CONFIRMATION THAT WE WERE AT FL290. THE CAPT STATED THAT WE WERE LEAVING FL290 FOR FL310 AND THAT HE HAD TFC IN SIGHT. THE CTLR STATED THAT WE WERE NOT CLRED TO CLB AND TO MAINTAIN FL290 AND HEADING 300 DEGS. WE IMMEDIATELY CORRECTED BACK TO FL290. THE CTLR THEN ASKED 'WHY WE HAD CLBED?' THE CAPT STATED WE WERE ASSIGNED HEADING 300 DEGS AND FL310. THE CTLR DISPUTED THIS STATING WE WERE ASSIGNED HEADING 300 DEGS BUT NOT CLRED TO CLB.