Computer modeling of the interface between two immiscible electrolyte solutions confirms that non-Nernstian behavior of cation-sensitive ion-selective electrodes (ISEs) can occur by the following molecular mechanisms: (i) extraction of weakly hydrophilic anions into the membrane, known as the anion effect or Donnan exclusion failure; (ii) leaching of the membrane's hydrophobic anion at low aqueous electrolyte concentrations; (iii) interference effects of competing cations. All three effects are known to occur under experimental conditions. Our theory employs a lattice-based self-consistent field model extended to include ion-carrier complexation by means of a multistate mechanism. The interface is created in the computer model by a self-assembling mechanism controlled by an unfavorable interaction parameter between the (PVC-lookalike) polymer of the membrane phase and the aqueous solution. Electrostatic potential profiles and charge-density profiles are available for the whole range of parameters considered in the computation of the calibration lines. The width of the polar/apolar interface is only a few molecular diameters thick, but at low ionic strength conditions the electric double layer extends far into both water and the apolar membrane phase.