This paper proposes a self-assembly method to construct a droplet interface bilayer (DIB) network. The DIB network has been developed for biological logical circuits or chemical microreactors, using incorporated membrane proteins. In this work, the DIB network was constructed by using multi-geometric Droplet-Boxes (DBs), which captured and stabilized an aqueous droplet in organic solvent. The multi-geometry enabled DB tessellation, and DIB network was constructed along the tessellation. Vibration triggered self-assembly of the tessellation with a help of capillary force. DIBs were verified by electrical measurement of alpha-Hemolysin (alpha HL). The proposed method demonstrated the potential of DIB network formation with good configurability and yield; hence, facilitates design of biological logical circuits based on DIB network.