The integration of semiporous membranes into poly(dimethylsiloxane) (PDMS) microfluidic devices is useful for mass transport control. Several methods such as plasma oxidation and manual application of PDMS prepolymer exist to sandwich such membranes into simple channel structures, but these methods are difficult to implement with reliable sealing and no leakage or clogging for devices with intricate channel features. This paper describes a simple but robust strategy to bond semiporous polyester and polycarbonate membranes between layers of PDMS microchannel structures effectively without channel clogging. A thin layer of PDMS prepolymer, spin-coated on a glass slide, is transferred to PDMS substrates with channel features as well as to the edges of the semiporous membrane by stamping. This thin PDMS prepolymer serves as "mortar" to strongly bond the two PDMS layers and seal off the crevices generated from the thickness of the membranes. This bonding method enabled the fabrication of an 8x12 criss-crossing microfluidic channel array with 96 combinations of fluid interactions. The capability of this device for bioanalysis was demonstrated by measuring responses of cells to different color fluorescent reagents.