When an ion moves across the interface of two immiscible electrolytes it moves together with the ion-induced protrusion of one solvent into the other. For an infinitely slow motion of an ion the height of the protrusion, h(eq), is a function of the position of the ion z. Due to a finite relaxation time the protrusion may not be able to spontaneously follow the motion of the ion, and this will cause slowing down of the ion transfer. The relaxation of the protrusion involves the movements of many solvent molecules and must be considered on the same footing as the motion along the coordinate of the ion. In this paper we develop a theory of such coupled motion which determines the kinetic laws of the ion transfer across the interface. When the equilibrium electrochemical potential for the ion has no barrier, the process of ion transport is purely diffusional and the effective diffusion coefficient may be evaluated as D-eff=k(B)T/{6eta[r(i)+(4/3)(h(max)/Lambda)L-2]}, where eta is the average viscosity of the liquids, r(i) is the Stokes radius of an ion, L and h(max) is the lateral size and the maximal height of the protrusion, and Lambda is the half width of the function h(eq)(z), which characterizes equilibrium ion-interface coupling. When there is a barrier, the theory recovers, depending on the height of the barrier, the mechanisms of ion transfer considered by Marcus or Gurevich-Kharkats-Schmickler. The effect of the nature of the ion and the solvents in contact is discussed.