Room-temperature ionic liquids (RTILs) have received significant attention as electrolytes due to a number of attractive properties such as their wide electrochemical windows. Since electrical double layers (EDLs) are the cornerstone for the applications of RTILs in electrochemical systems such as supercapacitors, it is important to develop an understanding of the structure–capacitance relationships for the EDLs of these systems. Here we present a theoretical framework termed “counter-charge layer in generalized solvents” (CGS) for describing the structure and capacitance of the EDLs in neat RTILs and in RTILs mixed with different mass fractions of organic solvents. Within this framework, an EDL is made up of a counter-charge layer exactly balancing the electrode charge, and of polarized generalized solvents (in the form of layers of ion pairs, each of which has a zero net charge but has a dipole moment—the ion pairs thus can be considered as a generalized solvent) consisting of all RTILs inside the system except the counter-ions in the counter-charge layer, together with solvent molecules if present. Several key features of the EDLs that originate from the strong ion–ion correlation in RTILs, e.g., overscreening of electrode charge and alternating layering of counter-ions and co-ions, are explicitly incorporated into this framework. We show that the dielectric screening in EDLs is governed predominantly by the polarization of generalized solvents (or ion pairs) in the EDL, and the capacitance of an EDL can be related to its microstructure with few a priori assumptions or simplifications. We use this framework to understand two interesting phenomena observed in molecular dynamics simulations of EDLs in a neat IL of 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]) and in a mixture of [BMIM][BF4] and acetonitrile (ACN): (1) the capacitance of the EDLs in the [BMIM][BF4]/ACN mixture increases only slightly when the mass fraction of ACN in the mixture increases from zero to 50% although the dielectric constant of bulk ACN is more than two times higher than that of neat [BMIM][BF4]; (2) the capacitance of EDLs near negative electrodes (with BMIM+ ion as the counter-ion) is smaller than that near positive electrodes (with BF4− as the counter-ion) although the closest approaches of both ions to the electrode surface are nearly identical.