Which part of the digestive system works like a partially permeable membrane?

A partially permeable membrane is a kind of membrane that selects the molecules or ions that pass through it by means of active or passive transport and depends on the substances and compatibility.

The membrane of the stomach  is quite tight and less permeable than the small intestinal mucosa,for example, or other ones that can be found in our body.  The gastric membrane is quite tight and this is useful because it limits the amount of secreted acid.

However the stomach needs permeable membranes as well. The mucosal lining of the intestinal tract is fundamental and it lines the digestive tract: It allows essential nutrients like vitamins, amino acids, etc... And serves as a barrier to undigested food particles, toxines and parasites.

So this means that though, that the membrane should never be really permeable otherwise this would lead to a weakened immune system, disorders or chronic diseases.

Hope this helps as a starting point to develop your research!