Imran, i too would just go with MDF, if you're worried about moisture, then you could go with a moisture resistant version. The nice thing about the MDF or HDF skin is the surface you have for painting is awesome and it's much lighter than regular MDF. There is however a lightweight version of MDF (Off the top of my head i believe it's called Ultralight and comes out of New Zealand) It's about the same weight as regular plywood, so is much easier on the back!
As David said, MDO is another option, just make sure to pick up some edgebanding to go with it, so you can do the edges in the same and have the same finish on them too once painted.
Derek, I would imagine the extra stiffness is likely as much a result of the lamination of the 3mm MDF as it is the MDF itself. If you look at how flimsy 3mm MDF is in that thickness, i'm going to say it's more bendy than the equivalent thickness of a solid timber, at least when you're flexing it along the grain. The glue joint thought will definitely add stiffness to it. That's partly why i laminate door stiles a lot. It adds lots of stiffness and results in a stile that's much less susceptable to movement.
Regards,
Bryce
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Bryce Comer