A fluid transport conduit for conveying ink-jet ink from a reservoir to a printhead in an ink-jet printer is provided. The fluid transport conduit comprises at least one inner layer, such as high density polyethylene, cyclic olefin copolymer, or polypropylene homopolymer, that is flexible and is a barrier to liquids, and at least one outer layer, such as nylon or polyvinyl alcohol, that is a barrier to air and is softer, or more compliant, than the inner layer, with the inner layer bonded to the outer layer. The two layers are advantageously co-extruded to form the fluid transport conduit.