Poly(dimethylsiloxane) (PDMS) and aromatic polyamide (aramid) multiblock copolymer (PAS) membranes containing greater than or equal to 55 wt % of PDMS were prepared. Their tensile strength, morphology, and oxygen permeation property were investigated. The observed high tensile strength of PAS with 55 wt % of PDMS indicates the presence of PDMS-aramid co-continuous phases with lamellar structures; furthermore, the microphase-separated structures of PAS membranes were observed by means of transmission electron microscopy. The overall oxygen permeation resistance of a conventional silicone rubber showed typical dependence on stirrer speed, which was derived from the macroscopic relationship between the membrane-liquid interfacial resistance and the stirrer speed. However, the overall oxygen permeation resistances of the PAS membranes were found not to simply depend on stirrer speed. Combining with the oxygen permeability of PAS in the case of a gas-membrane-gas system, the interface resistances of the membranes were evaluated. The interface resistances of the PAS membranes with the two-phase nature were more susceptible to the hydrodynamic parameter than that of the silicone rubber and became lower than that of the silicone rubber at higher stirrer speeds. The low interface resistance together with the high tensile strength of the PAS membranes enables us to provide highly oxygen permeable membranes in practical applications with a membrane-liquid interface.