Here's an example that my research group has been investigating. The cuttlefish bone, or simply "cuttlebone." This bone is not an actual "bone," but calcium carbonate based material that provides structural support as well as buoyancy control for cuttlefish underwater. Its micro-structure looks somewhat like a closed-cell foam, but much more complicated, with "pillars" and layered "septums." The porosity of this cuttlebone is about 90% or more, so it actually floats on water, but the cuttlefish can control buoyancy by control the water flowing in and out. Thin organic layers also appears in between the pillars. Its kinda difficult to describe the whole structure, so I'll attach a figure for you. The only thing that does not fit your request is that its not transparent, but if you demineralize it (remove the calcium carbonate by HCl or some acid), it would be transparent with only the organic frames.

honeycomb is one of the example I know which is a layered porous structure but I really don't know whether it is transparent or not.

Controlled pore glass. To be transparent, a material needs to Neither absorb nor scatter visible light. Most examples are either amorphous (like glasses) or single crystal. If the pores are not of a size to scatter light, it will remain transparent.

I think that the thin layers of asbestine wool processed with NaOH are somewhat transparent . It is possible to try if the material should be natural and if the canals (pores) should be not very narrow. However, asbest is harmful and the exhaust hood is necessary,

The best example is graphene

Very likely, there is another harmless and more technological way to solve your problem but it depends on the specificity of the task and it is our "now how".

"know how"

As for graphene: depending on circumstances.

What do you mean with "natural"

One of the best examples of transparent porous materials are silica aerogels.

It also depends on what you have in the pores, for example, some porous materials are only transparent when saturated with a fluid, because this changes the sacttering conditions...

"Natural", it is your term. It means that this substance is produced by Nature. If the natural origin of this material is not of necessity for you, you should formulate your question differently than it was formulated. However, my last word will be the same.

I am looking at our natural environment to have an example of layered porous materials. there is a lot of examples but I am looking for something that contain thin film layer in between porous layers.

Here's an example that my research group has been investigating. The cuttlefish bone, or simply "cuttlebone." This bone is not an actual "bone," but calcium carbonate based material that provides structural support as well as buoyancy control for cuttlefish underwater. Its micro-structure looks somewhat like a closed-cell foam, but much more complicated, with "pillars" and layered "septums." The porosity of this cuttlebone is about 90% or more, so it actually floats on water, but the cuttlefish can control buoyancy by control the water flowing in and out. Thin organic layers also appears in between the pillars. Its kinda difficult to describe the whole structure, so I'll attach a figure for you. The only thing that does not fit your request is that its not transparent, but if you demineralize it (remove the calcium carbonate by HCl or some acid), it would be transparent with only the organic frames.

Thanks a lot Chang. This was somewhat closer to what i was looking for. Do you have any published paper on it? But anyway, you have just added something in my toolbox. I really appreciate.

You're welcome, Rahman. We haven't published any papers yet, but we're going to submit one pretty soon, mainly focusing on the mechanical behaviors of this lightweight shield under loading in different directions. If you need additional information, just search for cuttlebone, there should be some research studies on the composition and some applications already :)

Really amazing material and structure, this cuttlebone, it'll very interesting to see your study of the mechanical behaviour, please keep me informed!!

This structure reminds some SEM pictures of the periostracum and the calcium carbonate layers I've have seen at the Harvard Museum of Natural History, I guess it'd possible to find something about this on internet.

Another biological structure having a layered and porous structure (maybe not transparent or at least transparent for certain wavelengths only) is that of plant leaves. You'll find plenty of SEM images of the leaves cross section in internet. there you have some non porous layers (cuticle, epidermis...), some low porosity layers (pallisade parenchyma) and some layers with a large porosity (>60%) and open-pore cell structure: an interconnected pore space, (spongy mesophyll).

No problem. I'll remember to update some information about the cuttlebone if any. However, since its not my own work but other group members' research studies, I'll have to ask for permission before sharing it here.

And you're right, plants offers a variety of cellular-structured materials, too. Besides leaves, plant stems and wood are also typical cellular materials. You can search for SEM images of cedar, oak, or balsa wood, which are somewhat "layered," but they look different from different directions, more or less a 3D structure.

Other cellular materials are feathers, bird beaks and porcupine quills, but I don't think they are anywhere near "layered" though.

In addition, I would suggest those who are interested in further information about cellular solids look up for books and papers by Lorna J. Gibson. Many of them are classic in this field.

Any poreless material can be optically transparnet also depending on how small the pores are! the scattering at the pore-host basin causes material becomes transluence, not perfert clear. So, if the pore is sufficient smaller comapred to light wavelength the scattering effect will be smearing out. In the extremem, materils are formed by atoms and there are always pores existing interstitially (the smallest), but non-conductive materials are clear, right?

There is a family of butterflies that has transparent wings. http://en.wikipedia.org/wiki/Greta_oto

Natural Mica comes in transparent layered form.. http://www.lampshadepro.com/Lamp-shades-are-real-mica-a-natural-mineral-mined-from-the-earth.html