We have considered the electrostatic field distribution near a soft pe
rmeable interface in an aqueous solution, taking into account the spat
ial variation of the dielectric permittivity within the framework of a
nonlocal electrostatic theory. We have analyzed the effect of the int
erface thickness as well as different combinations of the surface elec
tric charge and dipole densities. We have shown that the electric fiel
d potential is described in such systems by two exponential terms, one
of which is determined by Debye screening, and the other by the nonlo
cal polarization of the aqueous solution. For certain combinations of
the electric charge and dipole densities the potential can become nonm
onotonic. We have shown that, in addition to the electric charge and d
ipole densities, a significant parameter that determines the electric
field distribution in electric double layers is the interface thicknes
s. We discuss how the results obtained can assist in understanding mod
el lipid/protein systems, measurements of surface potentials, and surf
aces of biological membranes.