Lipid-bilayer-encapsulated nanoparticles (LBLENPs) or NP-supported LBL systems, such as protocells (which are lipid bilayer encapsulated mesoporous silica nanoparticles or MSNPs) have received extensive attention for applications like targeted drug and gene deliveries, multimodal diagnostics, characterization of membrane-geometry sensitive molecules, etc. Very often electrostatic-mediated interactions have been hypothesized to play key roles in the functioning of these LBLENPs. Despite that, very little has been done to theoretically quantify the fundamental electric double layer (EDL) electrostatics of such LBLENPs. In this study, we develop an EDL theory to describe the electrostatics of such LBLENPs. We show that the electrostatics is a manifestation of the charged/dielectric nature of the NP, LBL structure and charging, and the ionic environment in which the LBLENPs are present. We also establish that for certain conditions of charging of the NP one witnesses a most remarkable charge inversion like electrostatics within the LBL membrane or the NP itself. We anticipate that our findings will provide an extremely useful platform for better understanding the fabrication and functioning of such LBLENPs and discuss examples where our theory can be useful.