FLC SETS WRONG ASSIGNED ALT IN ALT ALERTER. ALTDEV OCCURS.

Narrative

ENRTE TO MILWAUKEE; WI; ATC GAVE US A CLRNC TO 10000 FT. THE FO (PNF) ACKNOWLEDGED THE ALT CLRNC TO 10000 FT. THE FO INCORRECTLY SET 11000 FT ON THE ALT ALERTER. AS THE PF; I CLBED TO 11000 FT AS THE ALT ALERTER SAID. AT 11000 FT; ATC INQUIRED ABOUT OUR ALT. WE SAID WE WERE CLBING TO 11000 FT DUE TO THE INCORRECT ALT ALERTER. AS PER OUR COMPANY CALLOUTS; WHEN A NEW ALT IS GIVEN; THE PNF SETS THE ALT ALERTER; BOTH PLTS POINT TO IT AND SAY IT OUT LOUD. AT THIS TIME; NEITHER ONE OF US CAUGHT THE MISTAKE. THE ALT ALERTER REMINDS US OF OUR ASSIGNED ALT. SINCE THE WRONG ALT WAS SET; WE CLBED TO THE WRONG ALT. WE HAD BEEN ASSIGNED 10000 FT BECAUSE ANOTHER ACFT WAS OVERTAKING US AT 11000 FT. THIS RESULTED IN BOTH ATC AND TCASII TFC ALERTS. WHEN ATC QUERIED US ABOUT OUR ALT; WE WERE MONITORING BOTH COM RADIOS. DURING DEP'S FIRST ATTEMPT; THE PNF THOUGHT IT WAS COMPANY OPS CALLING US ON COM #2. HE ACKNOWLEDGED THE SECOND ATTEMPT. BY THAT TIME; THE ASTRAJET HAD US IN SIGHT AND SAID TFC NO FACTOR. ADDITIONALLY; DURING ALL THIS CONFUSION; THE ASTRAJET WAS GIVEN A DEV HDG BY DEP AND THE PNF ACKNOWLEDGED THAT ASSIGNMENT. ATC SAID THAT WASN'T FOR US AND TO PROCEED ON COURSE. THE ASTRAJET DIDN'T NEED THIS HDG BECAUSE HE HAD US INSIGHT.