What's a word for the shape of the space among the trees in a forest?

The word "interstice" comes to mind. I'm a biology graduate and we referred to the space between the body's tissues as the interstitial space.

Interstice — ODO

(noun) usually interstices ; An intervening space, especially a very small one

"sunshine filtered through the interstices of the arching trees"

There is a concept in graphic design known as negative space which I think covers your intended meaning perfectly - Wikipedia has a decent article on it.

How about "interspace"?

noun
 ˈɪntəspeɪs/
1.
a space between things.
"the narrow interspaces between cells"

I think in all its simplicity "void" would also work well for your purpose.