An Air Carrier was cleared to cross a parallel runway during landing roll and as the aircraft's nose entered the runway the First Officer commanded an emergency stop because of departing traffic on that runway.

Narrative

During rollout after landing on 31C; Tower instructed us to taxi across 31R and then to contact Ground. We exited at Taxiway B and made the hard right turn onto Taxiway N to cross 31R. Once the nose of the plane turned enough so I could clear 31R visually; I saw something on the runway. I realized it was an aircraft on takeoff roll on 31R. I immediately and loudly stated; 'Stop; stop!' I reached to put my feet on the brakes. The Captain; without hesitation; stopped the aircraft; with the nose of the aircraft extending approximately ten feet beyond the hold short line to 31R. The jet taking off; which looked to be a twin-engine business jet; continued the takeoff and passed our position approximately two seconds after we stopped. We notified the Tower Controller of the event and requested acknowledgment of what we just reported. Tower cleared us to taxi across 31R (again) and to contact Ground. We contacted Ground; advised them of the event. Remaining taxi in and post flight procedures uneventful. It was unusual to be using 31R for departures; and the Tower Controller gave us the usual instructions for aircraft landing 31C. It was the combination of usual procedures and an unusual scenario that contributed to the Tower's error. I don't know what Tower could do to prevent this; or similar errors; from happening again. Sound procedures are in place; but inattention led to Tower's error.