The interconnection of different tissue-tissue interfaces may extend organ-on-chips to a new generation of sophisticated models capable of recapitulating more complex organ-level functions. Single interfaces are largely recreated in organ-on-chips by culturing the cells on opposite sides of a porous membrane that splits a chamber in two or by connecting the cells of two adjacent compartments through microchannels. However, it is difficult to interconnect more than one interface using these approaches. To address this challenge, we present a novel microfluidic device where cells are arranged in parallel compartments and are highly interconnected through a grid of microgrooves, which facilitates paracrine signaling and heterotypic cell-cell contact between multiple tissues. In addition, the device includes electrodes on the substrate for the measurement of transepithelial electrical resistance (TEER). Unlike conventional methods for measuring the TEER where electrodes are on each side of the cell barrier, a method with only electrodes on the substrate has been validated. As a proof-of-concept, we have used the device to mimic the structure of the blood-retinal barrier by co-culturing primary human retinal endothelial cells (HREC), a human neuroblastoma cell line (SH-SY5Y), and a human retinal pigment epithelial cell line (ARPE-19). Cell barrier formations were assessed by a permeability assay, TEER measurements, and ZO-1 expression. These results validate the proposed microfluidic device with microgrooves as a promising in vitro tool for the compartmentalization and monitoring of barrier tissues.