There is no way to Thicken in a particular direction. What you could do is this:
1. Create a sketch on a plane that is perpendicular to the edge that you want flat (so in this case, above or below your surface. Use Convert Entities to copy the outline of the surface onto the sketch.
2. Use Extend Surface to extend out your surface in all directions - essentially oversizing your surface.
4. Use an Extruded Cut with the sketch we made to trim the thickened surface down to the original size, complete with flat edges.