A D328 CREW; TAXIING FOR TKOF; CROSSED AN ACTIVE RWY WITHOUT A CLRNC.

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AS A FO; I GOT THE ATIS AND CLRNC; THEN CONTACTED GND CTL WHEN WE WERE READY TO TAXI. GND CTL GAVE US A ROUTING OF TXWY B; TXWY M; AND TXWY E FOR AN INTXN DEP AT VICTOR FOR RWY 19R. THE CAPT REPEATED THE TAXI INSTRUCTIONS AND I AGREED. HE THEN CALLED FOR THE TAXI CHKLIST. AFTER THE COMPLETION OF THAT CHKLIST; THE CAPT WAS GIVING ME SOME ADVISE ON XWIND TKOF TECHNIQUE SINCE IT WAS MY LEG TO FLY AND I HAD LOW TIME IN THE ACFT. RIGHT ABOUT AT THIS TIME; WE BOTH NOTICED A CPR JET DEPARTING FULL LENGTH ON RWY 19R. MY HEAD WAS INSIDE THE COCKPIT WHEN THE CAPT SAID CLR L; I THEN LOOKED TO THE R AND SAID 'CLR R;' NOT REALIZING THAT WE HAD PASSED INTXN V AND WERE XING AN ACTIVE RWY. THE TWR THEN NOTIFIED US OF OUR MISTAKE AND CLRED US FOR A FULL LENGTH RWY 19R DEP. CONTRIBUTING FACTORS: SEEING THE CPR JET USE THE FULL LENGTH OF THE RWY. NO ACTIVITY ON THE XING ACTIVE RWY (AT NO TIME WAS THERE ANY TFC ON OR LNDG ON THE RWY). THINKING THAT THE CAPT UNDERSTOOD THE ROUTING AND ME NOT VERIFYING HE WAS DOING IT CORRECTLY. CORRECTIVE ACTIONS: I BELIEVE THAT REMINDING THE CAPT OF OUR ROUTING WOULD HAVE PREVENTED THIS. ALSO; SEEING THE PRIOR ACFT USE THE FULL LENGTH MIGHT HAVE CAUSED US TO FORGET OUR INTXN DEP CLRNC. GND CTL COULD HAVE SEEN US PASSING INTXN V AND NOTIFYING US PRIOR TO XING ACTIVE RWY.