Poly(dimethylsiloxane) (PDMS) is one of the most common polymer materials for fabricating microfluidic devices for biological applications because of its unique properties. The hybrid micro devices made from PDMS and other polymer substrate materials are preferred due to their rapid prototyping, low cost, surface properties, and mechanical strength. However, the bonding between PDMS and other polymers is challenging because of the hydrophobic nature and low surface energy of PDMS. Here, we presented an approach to form a permanent and leakage free bond between PDMS microfluidic devices and polymer substrates using a PrimeCoat-Epoxy adhesive layer by selective stamp bonding. The enclosed cell adhesion and growth regions in the microfluidic device were kept intact without introducing adhesive bonding coatings. Additionally, the microfluidic devices can provide the flexibility to spatially and temporally control the cell microenvironment. The polymer substrate materials we chose are rigid polystyrene (PS) and flexible polyethylene terephthalate (PET) film, which are two common polymers used for cell cultures and biosensor applications. Our results demonstrated that the PrimeCoat-Epoxy bonding layer can withstand high flow rates and shear stresses and exhibited good biocompatibility. The cells growing inside the devices showed similar viability compared with conventional cell culture in dishes. In addition, the PrimeCoat-Epoxy adhesive bonding layer can bond to both hard and flexible polymer substrates, which is potentially important for developing large-scale integrated microfluidic assays.