Physically-encapsulated droplet interface bilayers are formed by confining aqueous droplets encased in lipid monolayers within connected compartments of a solid substrate. Each droplet resides within an individual compartment and is positioned on a fixed electrode built into the solid substrate. Full encapsulation of the network is achieved with a solid cap that inserts into the substrate to form a closed volume. Encapsulated networks provide increased portability over unencapsulated networks by limiting droplet movement and through the integration of fixed electrodes into the supporting fixture. The formation of encapsulated droplet interface bilayers constructed from diphytanoyl phosphocoline (DPhPC) phospholipids is confirmed with electrical impedance spectroscopy, and cyclic voltammetry is used to measure the effect of alamethicin channels incorporated into the resulting lipid bilayers. The durability of the networks is quantified using a mechanical shaker to oscillate the bilayer in a direction transverse to the plane of the membrane and the results show that single droplet interface bilayers can withstand 1-10g of acceleration prior to bilayer failure. Observed failure modes include both droplet separation and bilayer rupturing, where the geometry of the supporting substrate and the presence of integrated electrodes are key contributors. Physically-encapsulated DIBs can be shaken, moved, and inverted without bilayer failure, enabling the creation of a new class of lab-on-chip devices.