Screening for potential drug combinations presents significant challenges to the current microfluidic cell culture systems, due to the requirement of flexibility in liquid handling. To overcome this limitation, we present here an open-access microfluidic tissue array system specifically designed for drug combination screening. The microfluidic chip features a key structure in which a nanoporous membrane is sandwiched by a cell culture chamber array layer and a corresponding media reservoir array layer. The microfluidic approach takes advantage of the characteristics of the nanoporous membrane: on one side, this membrane permits the flow of air but not liquid, thus acting as a flow-stop valve to enable automatic cell distribution; on the other side, it allows diffusion-based media exchange and thus mimics the endothelial layer. In synergy with a liquid-transferring platform, the open-access microfluidic system enables complex multistep operations involving long-term cell culture, medium exchange, multistep drug treatment, and cell-viability testing. By using the microfluidic protocol, a 10 × 10 tissue array was constructed in 90 s, followed by schedule-dependent drug testing. Morphological and immunohistochemical assays indicated that the resultant tumor tissue was faithful to that in vivo. Drug-testing assays showed that the incorporation of the nanoporous membrane further decreased killing efficacy of the anticancer agents, indicating its function as an endothelial layer. Robustness of the microfluidic system was demonstrated by implementing a three-factor, three-level orthogonal screening of anticancer drug combinations, with which 67% of the testing (9 vs. 27) was saved. Experimental results demonstrated that the microfluidic tissue system presented herein is flexible and easy-to-use, thus providing an ideal tool for performing complex multistep cell assays with high efficiencies.