Owing to the heterogeneity of methane hydrate reservoirs in the South China Sea, hydrate and silty clay particles mostly exist in the form of interbedded reservoirs. Permeability is a decisive factor for the efficiency of interbedded methane hydrate deposits. Therefore, using montmorillonite as the simulated sediment material, permeability measurements of interbedded sediments with different methane hydrate distributions and effective stresses were carried out for the first time in this study. By comparing with homogeneous sediments, the permeability evolution of interbedded sediments under different hydrate distributions and effective stresses is explored, and the effect of methane hydrate dissociation on the permeability of interbedded sediments is analyzed. The results show that the permeability of interbedded sediments with different hydrate saturation levels has little difference and is almost the same as that of pure soil sediments. With the increase of effective stress, the porosity of methane hydrate interbedded sediments decreases and permeability damage is caused, but the final permeability damage is less obvious than that of homogeneous hydrate sediments. In addition, the gas slip effect exists in methane hydrate interbedded sediments. Moreover, the dissociation of methane hydrate causes clay swelling, which leads to the decrease of interbedded permeability, but the degree of permeability damage is lower than that of homogeneous sediments. The results of this study provide a theoretical basis for the development and utilization of interbedded methane hydrate sediments in the South China Sea.