We investigate the property of the bound states with an infinite number of classical turning points in the semiconductor superlattices (SL's) with the double-barrier and double-well structural defects. The anomalous parity sequence of these bound states violating the conventional parity rule is predicted. A physical mechanism on the origin of the bound states in the structural defect SL's, different from the mechanism addressed in the previous literature, is proposed. Based upon it, the parity anomaly can be interpreted very well. In addition, we also study the property of the optical transition in this system, for instance, the evaluation of the optical transition probability from the bound states to the bound states, from the bound states to the delocalized scattering states, and from the scattering states to other scattering states, in detail.