This paper investigates the wave propagation at the interface between the ocean and the ocean floor. The ocean floor is assumed to be composed of covered porous sediment with an underlying double-porosity substrate. For this purpose, plane wave reflection and transmission in the coupled water-porous sediment-double-porosity substrate system are analytically solved in terms of displacement potentials. Using numerical examples, the effects of the material properties of the underlying double-porosity substrate on the reflection coefficients are discussed in detail. Variations in pore and fracture fluid, fracture volume fraction, and permeability coefficients are considered. In addition, two cases of boundary conditions at the porous sediment-double-porosity substrate interface, i.e., sealed-pore boundary and open-pore boundary, are compared in the numerical calculations. Results show that material property variations in the double-porosity substrate may significantly affect the reflected wave in the overlying water if the sandwiched sediment depth is less than the critical value.