We have computed the dispersion curves of plate-mode waves propagating in periodic composite structures composed of isotropic aluminum cylinders embedded in an isotropic nickel background. The phononic crystal has a square symmetry and the calculation is based on the plane-wave expansion method. Along GammaX or GammaM directions, shear-horizontal modes do not couple to the Lamb wave modes which are polarized in the sagittal plane. Whatever the direction of propagation in between GammaX and GammaM, shear-horizontal modes convert to Lamb waves and couple with the flexural and dilatational modes. This phenomenon is demonstrated both through the mode splitting in the lower-order symmetric band structure and through the calculation of all three components of the particle displacements. The phononic case is different from the pure isotropic plate case where shear-horizontal waves decouple from Lamb waves whatever the direction of propagation.