Endothelial and epithelial cellular barriers play a vital role in the selective transport of solutes and other molecules. The properties and function of these barriers are often affected in case of inflammation and disease. Modelling cellular barriers in vitro can greatly facilitate studies of inflammation, disease mechanisms and progression, and in addition, can be exploited for drug screening and discovery. Here, we report on a parallelizable microfluidic platform in a multiwell plate format with ten independent cell culture chambers to support the modelling of cellular barriers co-cultured with 3D tumor spheroids. The microfluidic platform was fabricated by microinjection molding. Electrodes integrated into the chip in combination with a FT-impedance measurement system enabled transepithelial/transendothelial electrical resistance (TEER) measurements to rapidly assess real-time barrier tightness. The fluidic layout supports the tubeless and parallelized operation of up to ten distinct cultures under continuous unidirectional flow/perfusion. The capabilities of the system were demonstrated with a co-culture of 3D tumor spheroids and cellular barriers showing the growth and interaction of HT29 spheroids with a cellular barrier of MDCK cells.