Valve-like layers example in nature?
I don't know any-such continuous-membrane-material that can do so. But yes certain membrane-transport-proteins can do so.

Carrier proteins are normally highly specific about in which-direction to transport which molecule; and in general,  they are classified as uniporters, symporters and antiporters.  *



So an uniporter would be an accurate example of situation you are asking about. 

Carrier proteins those utilize ATP for pumping (those shows "primary active transport"), are also normally highly specific to direction. For example the Na+-K+pump and the H+ pump. 

Channel proteins too, sometimes show directionality, for example certain K+ channels ** such as inward-rectifying potassium channel



A potassium channel diagram showing the selectivity filter (diagram from The cell/ Cooper **, slightly edited: Na+ filter-out not shown, and the term 'selectivity filter' is labelled in image ).



KcsA potassium channel diagram from wikipedia. In its open-conformation out of the following; 



i.e. the third one, can conduct the K+ ion in a specific direction, because the pore-region is very specific- it allows K+ ion only to enter in the cell.


  Reference: 
  
  
  * Plant biochemistry by Hans Walter Heldt, 3rd edition, Academic Press-Elsevier, Paperback edition.
  ** The Cell, a molecular approach/ Cooper/ Sinauer and ASM press. 
  Harper's illustrated Biochemistry/ Murray, Bender, Botham, Rodwell, Well/ Lange and McGraw Hill.
  Wikipedia.