Melts of semiflexible AB diblock copolymers are studied using the wormlike chain model and self-consistent-held theory. The diblocks considered here are symmetric in composition and in A- and B-bIock flexibility. Under these conditions, the microstructure formed is lamellar. We find that an increase in molecular rigidity moves the order-disorder transition from chi N=10. 10.495 for Gaussian chains to chi N= 6.135 for rigid rods. In the ordered state, rigidity has little effect on the exponents that describe the scaling of the domain spacing and of the interfacial width with molecular weight. However, the proportionality constants are significantly affected. The spatial and orientational distribution of segments in the ordered microstructure is examined for a selection of conditions.