There's no 3rd dimension for textures shifting. The way a texture image is applied on a surface depends on the texture coordinates defined on a 3D model. Shifting the texture along X and Y allows to shift the image on all the surface of the 3D model (or a wall), but shifting the image and on a part of the model and not on another part is only possible if you change those texture coordinates which is not possible in Sweet Home 3D.

A solution for your problem is to use 2 different objects. But if you use walls, shift the texture along Y will work too.