Poly(dimethylsiloxane) (PDMS) and aromatic polyamide (aramid) multiblock copolymers (PASs) ranging from 26 wt % to 75 wt % in PDMS content were prepared and east into transparent, ductile, and elastomeric films from N,N’-dimethylacetamide solutions. The gas permeation properties and dynamic thermomechanical properties of the PAS films were investigated. It was found that the PASs containing < 75 wt % of PDMS had two-phase morphologies due to the great difference between the solubility parameters of the two components, in spite of the relatively low molecular weight of each segment. PASs containing greater than or equal to 35 wt % of PDMS showed the PDMS continuous phase and interfacial mixing occurred clearly between the two phases at the higher PDMS contents. PAS containing greater than or equal to 53 wt % of PDMS showed high enough gas permeability compared with conventional silicone rubbers. The gas permeation properties can be well predicted by the PDMS contribution to the continuous phase rather than by the modulus behaviors alone.