We numerically investigate the flight dynamics and aerodynamics of a two-dimensional model for the jellyfishlike ornithopter recently devised by Ristroph and Childress [L. Ristroph and S. Childress, J. R. Soc. Interface 11, 20130992 (2014)]. This simplified model is composed of two rigid thin foils which are forced to pitch in antiphase fashion. The Navier-Stokes equations for the fluid and the dynamics equations for the flyer are solved together in the simulations. We first consider the constrained-flying condition where the flyer model is only allowed to move in the vertical direction. The influences of the control parameters on the hovering performance are studied. With the variations in parameter values, three different locomotion states, i.e., ascending, descending, and approximate hovering, are identified. The wake structures corresponding to these three locomotion states are explored. It is found that the approximate hovering state cannot persist due to the occurrence of wake symmetry breaking after long-time simulation. We then consider the free-flying condition where the motions in three degrees of freedom are allowed. We study the postural stability of a flyer, with its center of gravity located at the geometric center. The responses of the flyer at different locomotion states to physical and numerical perturbations are examined. Our results show that the ascending state is recoverable after the perturbation. The descending state is irrecoverable after the perturbation and a mixed fluttering and tumbling motion which resembles that of a falling card emerges. The approximate hovering state is also irrecoverable and it eventually transits to the ascending state after the perturbation. The research sheds light on the lift-producing mechanism and stability of the flyer and the results are helpful in guiding the design and optimization of the jellyfishlike flying machine.