NMAC AFTER ALT DEV ALT OVERSHOT.

Narrative

INBOUND TO LAX; WHILE TALKING TO BUR APCH WE WERE TOLD TO DSND AND MAINTAIN 6000 FT. I REPLIED THAT WE WERE GOING DOWN TO 6000 FT. WE NOTICED A GA ACFT COMING THE OPPOSITE DIRECTION; SAME HDG BUT NO TFC CALL FROM THE CTLR. THE CTLR CALLED OUT 'ACR X STOP;' THEN STOPPED TALKING; I REPLIED THAT WE HAD THE ACFT IN SIGHT; HE THEN GAVE US A HDG AND TURNED US OVER TO LAX (SO-CAL) APCH. UPON LNDG WE WERE ASKED TO CALL BURBANK APCH CTL; WHERE THE SUPVR ADVISED ME THE ALT. WE HAD BEEN ASSIGNED WAS 7000 FT NOT 6000 FT. HE ADVISED ME TO BE MORE CAREFUL; I EXPLAINED THAT I HAD ASKED MY PARTNER (FO) AND HE ALSO RECALLS BEING ASSIGNED 6000 FT. THE SUPVR SAID HE HAD LISTENED TO THE TAPE AND HIS CTLR HAD SAID 7000 FT AND I REPLIED WITH 6000 FT. HOWEVER THE CTLR DID NOT CATCH THE READBACK AND FAILED TO NOTICE US GO BELOW 7000 FT. WE BELIEVE WHAT CAUSED THE PROB WAS ANOTHER ACFT THAT WAS HAVING RADIO PROBS AND KEPT 'STEPPING ON' OTHER XMISSIONS. I AM NOT SURE IF THE CTLR WAS DISTR BY THIS PROB; BUT WE BOTH WERE SURE WE HAD BEEN ASSIGNED 6000 FT. I BELIEVE A LITTLE MORE ATTN TO DETAIL ON BOTH PARTIES MIGHT HAVE ALLEVIATED THIS PROB.