FLC OF A B737 OVERSHOT CLB ALT DUE TO MISUNDERSTANDING OF ATC'S LAST CLRNC. AFTER FLC QUESTIONED ATC; ATC REVISED THEIR CLRNC TO A HIGHER ALT.

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I WAS FLYING AND CLBING OUT OF 11000 FT FOR 13000 FT WHEN DEP TOLD US TO FLY 280 KT SPD CLB TO X30(?) AND CONTACT ZAU ON 120.35 FO MISUNDERSTOOD SPD AS 300 KTS VERSUS 280 KTS AND READ BACK 300 KTS. ATC CORRECTED SPD; FO MISSED READBACK ON ALT AND FREQ. I THOUGHT WE WERE CLRED TO FL230 AND CONTINUED CLB. AT THIS POINT; I ASKED FO TO VERIFY ALT AS ALT REMINDER WAS STILL AT 13000 FT. HE CHKED IN WITH CTR AND SAID 13000 FT CLBING TO FL230; 280 KTS. CTR SAID; 'NEGATIVE; CLRED TO 13000 FT.' FO SAID WE WOULD RETURN TO 13000 FT (ALT AT TIME APPROX 13700 FT). CTR SAID; 'SINCE YOU ARE ALERADY THROUGH IT; CONTINUE TO 15000 FT.' WE DISCUSSED THE EVENT AND DETERMINED THAT THE SPD 280-300 KTS; 13000 FT; 120.35 HAD NOT BEEN CLR AND THE FREQ WAS SO CONGESTED THAT WE WERE UNABLE TO INQUIRE IN A TIMELY MANNER. I THINK THAT THE 120.35 HAD SOUNDED LIKE FL230 TO ME. I FEEL THAT THE EVENT COULD BE PREVENTED BY MY STRICTER COMPLIANCE WITH THE ALT REMINDER; LESS FREQ CONGESTION AND CLRER RADIOS. I CALLED THE ZAU SUPVR AND HE SAID THAT THEY HAD NO CONFLICTS OR RPTS DURING THAT PERIOD. I TOLD HIM TO THANK THE CTLR FOR HIS HELP AND WE ALL AGREED THAT THE BUSY ENVIRONMENT AND CONGESTION IS REACHING PEAK SATURATION.