Unusual dispersion properties are observed in a phononic crystal of nylon rods in water when the lattice constant is adjusted so that Bragg and hybridization gaps overlap in frequency. On the basis of experimental and numerical analyses of time-dependent transmission and spatial field maps, the presence of two coexisting propagation modes of similar amplitude is demonstrated near the resonance frequency. This phenomenon is attributed to the coupling of the rod resonances arranged in a triangular lattice, with phase shifts driven by the Bragg condition.