Following a practice instrument approach, the student pilot and flight instructor intended to perform a touch-and-go maneuver. During the landing roll the instructor informed the student to retract the twin-engine airplane’s flaps; however, the student inadvertently moved the landing gear retraction/extension handle to the “up” position. Although, the instructor moved the landing gear handle back to the “down” position, the airplane’s nose landing gear collapsed. The airplane continued down the runway about 240 feet before exiting the right side of the runway into the grass. The airplane came to rest in a nose down position and all three occupants were able to exit unassisted. An examination of the airplane by maintenance personnel after the accident revealed that the right wing sustained structural damage. There were no reported anomalies with the airplane’s landing gear prior to the accident.