Following a 25 nautical mile cross-country night flight the private pilot performed a full stop landing. The pilot then departed and stayed in the airport traffic pattern for a second landing. During touchdown the airplane impacted the runway hard and bounced back into the air before settling back on the runway. One of the two passengers reported hurting her back during the hard landing so the pilot taxied to and shut down the airplane at the airport’s fixed base of operations (FBO). After examining the airplane for damage and finding none, the pilot elected to depart with his passengers and successfully flew back to their originating airport. Approximately three months later during the airplane’s annual inspection, the engine firewall was found to be damaged. The pilot later reported that there were no malfunctions or defects with the airplane’s flight controls that contributed to the hard landing.