Aqueous droplets submerged in an oil-lipid mixture become enclosed by a lipid monolayer. The droplets can be connected to form robust networks of droplet interface bilayers (DIBs) with functions such as a biobattery and a light sensor. Such DIB networks might be used as model systems for the study of membrane-based biological phenomena. In this study, we develop and experimentally validate an electrical modeling approach for DIB networks by applying it to describe the current flow through a simple network containing protein pores and blocking molecules. We demonstrate the use of SPICE (Simulation Program with Integrated Circuit Emphasis) for simulating the electrical behavior of DIB networks. The modular and scalable nature of DIB networks should enable a straightforward extension of the analysis presented in this paper to large, complex networks.