AN A320 FLT CLBS 600 FT ABOVE ITS ASSIGNED ALT WHEN CAPT GETS CONFUSED AS TO THE ALT ASSIGNMENT FROM AN OVERLOADED DEP CTLR AT ORD; IL.

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DEPARTED ORD RWY 32L; T10 INTXN. TURNED L TO 220 DEG HDG; CLBING TO 5000 FT AND TOLD TO CONTACT DEP CTL 127.4. FO FLEW AND I WAS PNF. DEP CTLR TALKED WAY TOO FAST GIVING ALTS AND HDGS TO SEVERAL ACFT; ONE RIGHT AFTER THE OTHER. WE WERE CLRED TO 6000 FT AND HDG 160 DEGS. I REPLIED EITHER 6000 FT OR 16000 FT; BUT SET 16000 FT IN THE MCP. CLBING THROUGH 4700 FT AT 4000 FPM WE GOT A TA FROM AN ACFT IN OUR 2 O'CLOCK POS; 3000 FT ABOVE. THEN WE BROKE ABOVE THE CLOUDS; SAW THE ACFT PASS OFF TO OUR R. I WAS TRYING TO CONFIRM OUR CLRNC WITH DEP; BUT COULD NOT GET A WORD IN. FINALLY; DEP SAID 'YOU ARE CLRED TO ZERO SIX THOUSAND FT AND HDG 160 DEGS.' AS WE PASSED 6000 FT; I CALLED TO THE FO TO LEVEL OFF; BUT 16000 FT WAS STILL IN THE ALT WINDOW. AT 6600 FT; THE FO STARTED TO DSND BACK TO 6000 FT WHEN I ASKED DEP AGAIN TO SAY OUR CLRNC. HE THEN SAID 'YOU WERE CLRED TO 6000 FT; BUT NOW YOU ARE CLRED TO 16000 FT AND HDG 140 DEGS.' THIS ALL OCCURRED IN ABOUT 30-45 SECONDS. SUPPLEMENTAL INFO FROM ACN 535386: THE RAPID-FIRE INSTRUCTIONS WITH NO TIME TO READ BACK MADE COMS DIFFICULT.