I'm guessing you're looking at resawing thicker boards down to something suitable for dolls houses on the bandsaw and then getting the boards flat and square on the planer?
Very thin (and non-flat) timber is likely to flex as in needs to be pushed down very firmly onto the planer. There is also a risk of very thin timber shattering if there's a defect in the timber.
If you had a planer/thicknesser you could flatten the thick board on the planer, resaw a the first thin board from it, put that thin board on a wooden sledge and put it through the thicknesser. Then plane up the sawn face on the thick baord and repeat the process.
You could of course do the same thing with a rigid backing on the thin board with the planer, but with your fingers in close proximity if the the thin board breaks up.
A thicknesser with its power feed will also produce better results than the planer. It's common to get a good face on the planer, thickness it to a second flat face, flip it over, and let the thicknesser do its magic on the original face.
I wonder if the final thicknessing operations would be better suited to a belt sander with a fine grade grit - with the object board backed to somthing bigger as you suggest. You may need a mandrel or some kind of preset depth indication to tell you when you've reached your target thickness
I have an Electra-Beckum planer-thicknesser that works well thicknessing down to 4mm (I did some beech today). I wouldn't dream of using the planer on anything that thin though - too dangerous. I'd re-saw to say
8mm, then thickness it down to 4mm. If I wanted thinner, I'd glue some sandpaper to an 18mm ply board and pass that with the stock on it through the thicknesser - the sandpaper is to stop stock slipping as the knives work. On the other hand aero industry 1mm plywood is good and always flat.
I think the ideal machine for very thin stock would be a belt sanding machine like this:
You're better off working on tuning your bandsaw so that resawing is reliable and gives a good surface finish, then using any "thicknesser" as only a surface finishing step. Use either a drum sander (probably in a home-built jig) or a converted spokeshave iron, as described in one of Bob Wearing's "Jigs and gadgets" books.
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