Thickness for displacement mesh

Hi, I am trying to give a thickness for the displacement mesh I made. I want to give it a thickness and have the backside flat as wall. Is there anyway to do it?

not automatically if you want it flat.

if it can be not planar, you can simply use mesh offset with the solid option ticked. (the mesh will be HEAVY)

if it has to be flat, you could create a simple planar surface that represents the back surface, then mesh it, then repair the gaps between the front and rear surface like I did in this video.