ALTDEV ALT OVERSHOT.

Narrative

I WAS PIC FROM DAL TO HOU. I WAS FLYING THE ACFT DURING CLBOUT WHEN THE FO CHKED OFF FREQ TO GET THE ATIS WHILE I WAS CLBING TO 23000 FT. I RECEIVED CLRNC (I THOUGHT) TO FL290. I RESPONDED AND SET 290 IN MY ALT ALERT. AS WE WERE CLBING TO FL270; THE FO CHKED BACK ON AND ASKED IF I WAS SURE THAT THE CLRNC WAS TO FL290. HE THOUGHT IT WAS TO FL270. SINCE HE HAD CHKED OFF; I DID NOT THINK HE HAD HEARD THE CLRNC; SO I ASSURED HIM THAT WE HAD BEEN CLRED TO FL290. AFTER LEVELING AT FL290; I STARTED HAVING SECOND THOUGHTS AND STARTED WATCHING THE TCASII FOR POSSIBLE CONFLICTING TFC. SHORTLY; I SAW AN ACFT COME INTO VIEW 15 MI AHEAD XING R TO L. I TOLD THE FO TO TELL CTR THAT WE WERE AT FL290. HE DID SO; AND CTR IMMEDIATELY CLRED US TO FL270 AND TO EXPEDITE OUT OF FL280. WE COMPLIED AND LEVELED AT FL270 MORE THAN 10 MI FROM THE TCASII TARGET. I DID NOT KNOW THAT THE FO HAD HEARD THE CLRNC EVEN THOUGH HE WAS COPYING THE ATIS. HE THOUGHT HE HAD HEARD FL270 AND INDICATIONS ARE THAT HE WAS PROBABLY RIGHT. I SHOULD HAVE LEVELED AT FL270 AND CONFIRMED THE CLRNC. I AM STILL NOT ABSOLUTELY CERTAIN THAT WE LEVELED AT THE WRONG ALT AND I DON'T KNOW IF I READ BACK 270 OR 290. THIS WAS A CASE HOWEVER; WHEN THE TCASII PROVED VERY USEFUL IN AVERTING WHAT COULD HAVE BEEN A CONFLICT.