A seal member having a thermoplastic body for an electrochemical cell containing a nonaqueous organic solvent electrolyte. In particular, the seal member is preferably one or more of (a) a seal located between a cell container wall and a cell cover and (b) a seal of a vent assembly, more particularly a ball vent assembly. The seal member has a composite construction including one or more vapor transmission barrier layers disposed on a portion of the thermoplastic body.