In a recent paper Nayfeh et al. [1] presented theoretical and experimental results for the propagation of longitudinal waves in a composite whose microstructure was large enough to cause observable velocity dispersion. Only wave propagation along the fiber axis of a uniaxial laminate was considered. A reflection coefficient was also derived for the case of normal incidence and parallel to the fibers. For ultrasonic inspection applications, what is required is the ability to analyze situations in which the wave is incident at arbitrary angles. Analysis of such general situations are, however, difficult to treat. A relatively simpler two-dimensional composite, which has been analyzed for an off-normal incident angle [2], consists of a bilaminated model with layers bonded and stacked normal to the x3-direction. The structure occupies the half-space x2 ≥ 0 as illustrated in Fig. 1. The composite is immersed in water such that the x2-direction is normal to the fluid-composite interface and the wave is incident from the fluid in the x1-x2 plane. For this model the reflection coefficient and the characteristic equation for the propagation of fluid-composite interfacial waves was calculated. The results reported in [2] are also restricted such that the individual composite components are isotropic.