The commercial pilot was on her second flight of multi-engine flight instruction as she completed an approach and flared the airplane for landing. The instructor said his attention was "outside" as he monitored the airplane's height, drift, runway alignment, and guarded the throttles. The airplane suddenly landed hard, bounced back into the air, and did not respond as expected to the instructor's remedial actions. The engines responded to an increase in throttle for a go-around, but there was no corresponding increase in thrust. The airplane drifted to its left, and the instructor chose to close the throttles, and perform a controlled landing. The airplane departed the runway surface and came to rest in the grass infield with substantial damage to the fuselage forward of the cockpit. According to the instructor, there were no deficiencies in the performance and handling of the airplane. The student pilot had experienced a negative habit transfer from her experience in the airplane she was accustomed to flying as the configuration of its throttle quadrant differed from the accident airplane and she had inadvertently reduced (feathered) the propellers rather than reducing the throttles while landing.