AFTER LNDG AT ZZZ; CREW READS BACK TAXI INSTRUCTIONS INCORRECTLY AND CROSS RWY WHILE TFC IS DEPARTING.

Narrative

AFTER LANDING ON RWY PL AT ZZZ; WE CLRED ONTO TXWY A; TWR ADVISED TO GIVE WAY TO AN ACFT Y ON TXWY B AND TO HOLD SHORT RWY PC FOR DEP CONTACT GND ON 123.0 ON TXWY A AFTER CROSSING RWY PC. MY FO READ BACK CLRNC TO CROSS RWY PC AND TO CONTACT GND ON 123.0 ON TXWY A AS WE WERE CROSSING RWY PC. I HEARD TWR TELL ACFT Z TO ABORT TKOF. I SAW ACFT COMING AND ADDED POWER TO FINISH CROSSING AS FAST AS POSSIBLE. ACFT Z CONTINUED THE TKOF AND WAS AIRBORNE WELL BEFORE TXWY A BY 100 - 200 FT AND MY ACFT WAS STOPPED ON THE TXWY AT THE INTERSECTION OF TXWY A AND B; WELL CLEAR OF ACTIVE RWY. WE WERE TOLD TO CONTACT GND ON 123.0 AND CONTINUED TAXI TO GATE. ATC NEVER SAID ANY MORE ABOUT INCIDENT; AND DID NOT ASK US TO MAKE CONTACT BY PHONE. COMMUNICATIONS WERE VERY BUSY AND CONFUSING AT THE TIME; SEVERAL JAMMED TRANSMISSIONS ADDED TO CONFUSION. I ASKED THE FO IF HE WAS SURE WE WERE CLRED TO CROSS AND HE SAID IT WAS. SUPPLEMENTAL INFO FROM ACN 508160: WE WERE STARTING TO CROSS RWY PC AND WE SEE DEPARTING TFC ON RWY PC. THE TWR CTLR PANICKED AND TOLD US TO EXPEDITE ACROSS RWY PC AND HE CANCELLED THE TAKEOFF CLRNC FOR THE DEPARTING TFC. I HEARD AND READ BACK TWR INSTRUCTIONS. THE SAME TWR CTLR WAS HANDLING TOO MUCH TFC AND THE ARPT WAS VERY BUSY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED AFTER THE INCIDENT HE FILED A RPT WITH HIS CHIEF PLT. HE SAID THE CHIEF PLT DISCUSSED THE INCIDENT WITH THE FACILITY MANAGER AND WAS TOLD THAT AN OPERATIONAL ERROR MAY HAVE OCCURRED.