THE PURPOSE OF THE FLIGHT WAS TO GIVE DUAL INSTRUCTION TO THE OWNER/STUDENT WHOSE MULTI-ENGINE RATING WAS LIMITED TO CENTERLINE THRUST MODELS. THE STUDENT WAS FLYING THE AIRCRAFT ON THE TAKEOFF ROLL WHEN THE COCKPIT DOOR BECAME AJAR. THE AIRCRAFT WAS NEAR LIFT-OFF SPEED AND THE STUDENT INTENDED TO CONTINUE TAKING OFF. THE INSTRUCTOR REPORTED THAT HE GAVE TWO COMMANDS TO ABORT, BUT THEY WERE NOT HEARD BY THE STUDENT DUE TO NOISE COMING FROM THE OPEN DOOR. THE INSTRUCTOR RETARDED THE THROTTLES TO IDLE POWER; HOWEVER, THE AIRCRAFT BECAME AIRBORNE AND BOUNCED ON THE RUNWAY BEFORE THE STUDENT REAPPLIED THE POWER AND REGAINED CONTROL OF THE AIRCRAFT. THEREAFTER, THE STUDENT LANDED FROM A FULL CIRCUIT APPROACH WITHOUT FURTHER INCIDENT. HOWEVER, THE RIGHT PROP WAS DAMAGED AND WRINKLES WERE FOUND ON RIGHT WING AND FUSELAGE.