Dawn:
I, too, am in Zone 7 -- 7b to be more precise. Under my mixed oaks and
pines, I have azaleas, winter daphne, a tiny Japanese maple (it's out
hear the western edge of the drip-line of the larger trees), lenten
roses, foam flower (tiarella cordifolia), green-and-gold, hostas,
several varieties of ferns, etc., etc.

If it's a possibility, you should try to visit Juniper Level Botanic
Gardens www.plantdelights.com, the home of Plant Delights Nursery.
While Plant Delights has many tempting plants for sale, I'm recommending
visiting because of the extensive shade gardens, and it's here in Z7.
Looking at what they have done would be a great inspiration for you!

Dawn wrote:

About half of our new yard is under tall elm and oak trees. Although
the previous owner was fighting to keep grass growing under there we
are thinking of going with more natural plants and bushes.

I know azaleas and rhododendron grow naturally in the woods, any other
suggestions (we live in Zone 7)?

TIA,
Dawn