Hi Marc, you'll probably want to use a welded mesh so that the pieces don't jiggle apart.

Also are you just using the default UV coordinates for that displacement mapping? That's probably what is causing your unwanted disruption at the seam between the top surface and the side.

You'll need to get a continuous UV mapping on your shape if you want the displacement map to also behave as a continuous looking thing across the whole model.

If you were to apply a regular image map to that piece, that would probably show you a similar break between the pieces as well.

I think it's likely that the UV mapping on your other piece is the reason why it behaves how you want, not particularly something to do with subdivision surfaces...

- Michael