Is there a word for "air can pass through it"?

If light can pass through an object, or if you can see through it, it is transparent.

Is there a similar word for "air can pass through", or you can breathe through an object? This adjective would be used to describe a screen door, or certain types of fabric.

Solution 1:

permeable if the pores are small

allowing liquids or gases to pass through; capable of being permeated; penetrable; especially: having pores or openings that permit liquids or gases to pass through

breathable if it's a fabric

Permitting air to pass through: a breathable fabric.

I don't know what to call this property in a screen door...

apologies to @James McLeod - I didn't read the entire question and jumped on permeable.

Solution 2:

Rather to my disgust (as some who grew up reading a great deal of science fiction), the industry-accepted term for this is "breathable."

I know this is ugly and misleading, but it's the word.