The dielectric permittivity across the liquid-liquid interface presents an intrinsic response, with respect to the instantaneous interface reference. We hypothesize that dielectric responses across the nonpolar and polar liquid-liquid interfaces have different behaviors and underlying mechanisms. Molecular dynamics simulations were used to compare and contrast the dielectric response of a nonpolar (1,2-dichloroethane/water) and a polar (1-octanol/water) liquid-liquid interface system. We found that the enhanced dielectric permittivity at the nonpolar interface is attributed to the increased water dipole orientation and polarization density. In the case of the polar interface, strong association of the immiscible solvents inhibits the molecular dipole orientation, counteracting the effect from the enhanced surface water polarization density and resulting in a standard dielectric response. Detailed knowledge of the hydrogen bond networks and molecular dipole orientation with respect to the specific instantaneous interfacial and bulk regions reveals the effect of molecular proximity and the interaction with the opposing interfacial molecules on the mechanism of the dielectric permittivity response across the liquid-liquid interface phase boundary.