The commercial certificated pilot/flight instructor was providing instruction to a student pilot on a CFR Part 91 local flight. The instructor reported that during the landing roll, a 7 knot right crosswind pushed the tail of the airplane left, and the nose veered to the right. The student attempted to correct the turn with left brake application, but was unable to prevent the airplane from departing the right side of the runway. The left horizontal stabilizer struck a runway sign, damaging the stabilizer and the left elevator.