Recent advancements in micro/nanofluidics have facilitated on-chip microscopy of cellular responses in a high-throughput and controlled microenvironment with the desired physicochemical properties. Despite its potential benefits to combination drug discovery, generating a complete combinatorial set of concentration gradients for multiple reagents in an array format remains challenging. The main reason is limited layouts of conventional micro/nanofluidic systems based on two-dimensional channel networks. In this paper, we present a device with three-dimensional (3D) interconnection of micro/nanochannels capable of generating a complete combinatorial set of concentration gradients for two reagents. The device was readily fabricated by laminating a pair of multilayered monolithic films containing a Christmas tree-like mixer, a cell culture chamber array, and through-holes, all within each single film. We assessed the reliable generation of a full-combinatorial concentration gradient array and validated it by using numerical analysis. We applied the proposed device to test the antibiotic susceptibility of bacterial cells in a convenient one-step manner. Furthermore, we explored the potential of the device to accommodate the arrayed complete combinatorial set for two or more drugs, while extending the capabilities of our laminated object manufacturing method for realizing 3D micro/nanofluidic systems.