The present invention generally relates to a wet wipe or sheet that is suitable for contacting the skin and that has a stratified wetting composition therein. More specifically, the present invention related to a wet wipe, which may optionally be an ion-triggerable, water-disintegratable wipe, wherein the organic phase, and more particularly one or more components of the organic phase, of the wetting composition is concentrated near the surface of the wipe, and the aqueous phase of the wetting composition is concentrated in the bulk of the wipe. The present invention is further directed to a number of processes for preparing such a wet wipe. For example, in one embodiment an emulsified wetting composition is applied to a fibrous substrate of the wet wipe, and then treated to destabilize the emulsion. In an alternative embodiment, an emulsified wetting composition may be destabilized prior to it being applied to the fibrous substrate. As a result of the destabilization, the emulsion undergoes phase separation after being applied to the fibrous substrate.