Biomolecular networks formed from droplet interface bilayers (DIB) use principles of phase separation and molecular self-assembly to create a new type of functional material. The original DIB embodiment consists of lipid-encased aqueous droplets surrounding by a large volume of oil contained in a shallow well. However, recent results have shown that, by reducing the amount of oil that separates the droplets from the supporting substrate, physically-encapsulated DIBs display increased durability and portability. In this paper we extend the concept of encapsulated biomolecular networks to one in which phase separation and molecular self-assembly occur entirely within internally-structured reservoirs of a solid material. Flexible substrates with 200μm wideby-200μm deep internal microchannels for holding the aqueous and oil phases are fabricated from Sylgard 184 polydimethylsiloxane (PDMS) using soft-lithography microfabrication techniques. Narrowed apertures along the microchannels enable the use of the regulated attachment method (RAM) to subdivide and reattach lipid-encased aqueous volumes contained within the material with an applied external force. The use of perfluorodecalin, a fluorocarbon oil, instead of hexadecane eliminates absorption of the oil phase into the PDMS bulk while a silanization surface treatment of the internal channel walls maximizes wetting by the oil phase to retain a thin layer of oil within the channels to provide a fluid oil/water interface around the aqueous volumes. High-quality 1,2-diphytanoyl-sn-glycero-3-phosphocholine (DPHPC) lipid bilayers formed within the prototype substrates have electrical resistance between 1 − 100GΩ, enabling the measurement of single and few-channel recordings of alpha-hemolysin (αHL) and alamethicin proteins incorporated into the bilayers.