We report fabrication and characterization of microfluidic devices made of thermoplastic and elastomeric polymers. These hard-soft hybrid material devices are motivated by the combined need for large scale manufacturability, enhanced barrier properties to gas permeation and evaporation of aqueous solutions compared to poly(dimethyl siloxane) (PDMS) devices, and compatibility with deformation-based actuation. Channel features are created on rigid polymers such as polyethylene terephthalate glycol (PETG), cyclic olefin copolymer (COC), and polystyrene (PS) by hot embossing. These "hard tops" are bonded to elastomeric "soft bottoms" (polyurethane (PU) or PDMS-parylene C-PDMS) to create devices that can be used for microfluidic cell culture where deformation-based fluid actuation schemes are used to perfuse and recirculate media. The higher barrier properties of this device compared to PDMS devices enable cell culture with less evaporation and creation of hypoxic conditions.