I have sort of the same thing but with 3 ugly Bradford pear trees. The area doesn t get much sun at all but it isn t dark. I have Hydrangea Annebelles,oakleaf hydrangeas,creeping jenny,couple diferent epimediums,hardy begonias, solomons seal, hostas of course and wild gingers

Thanks for that.

I should have added that this is on the northwest corner, so the trees get sun most of the day.

The RIVER birches tend to soak up most of the moisture and so a lot of ferns would struggle(some of the Polystichums such as tassle fern are a bit better in drier soil), and the hostas would need extra water too. The oakleaf hydrangea tolerates more dryness than the other hydrangeas. Vinca minor isn't picky and would provide lavender flowers in spring. Of course lilies of the valley tolerate both shade and dryness.

I have three single trunked river birch planted in a triangle along the fence where huge amounts of slow moving water collects from the neighbors steep roof runoff. In the past that collecting water compacted the topsoil which caused the area to sink slightly as the silty soil compressed, and the slightly lower elevation area caused eroded areas to develop.

The comments above about groundcovers that can handle dry conditions under birch trees are great when rainfall is scarce; however, are any of these or other suggestions also able to survive during inches of standing water events which commonly occur during the spring and fall heavy rain seasons?

IF the trees are not mature, and there is some morning or afternoon sun under them, daylillies will take some extra water, and you could try spiderwort as well. Mazus will also take water, it's a low groundcover.

Pachysandra would be a no brainer. It will form a compact dense carpet within a season or two. Can handle all kinds of conditions.