Need advice about tiled terrain

Heello guys i’m working on a tiled ground and wanted to have some advices from some people who have a good experience with JMonkey,
the floor is tiled, and each tile can have a different height, so autmatically I think about heightmap arrays…
What I was thnking is that each object on the floor affects the heightmap, so if someone puts a chair or a table on the floor, the heightmap is affected , so the players can walk on the table, climb onthe furnitures and thinngs like that.

is it a good approach? like every object on the ground affects the height map.
has anyone ever worked on something similar?

My first thought here is that if a game object has a collision mesh then climbing on top of it should work more or less ‘out of the box’… provided your player controller is set up etc.