I have a large riverbirch on the corner of my garden and I've had success with Astible, Hosta, Bachler Button, Colubine, Ferns and Phlox. The Phlox flowers a little later then the others though so you'll have color later in the summer, early fall.
Kim

Hellebore for early bloom, spigelia, dwarf sweet box (Sarracocca humilis). Also hardy geraniums, amsonia and jacob's ladder if not heavy overhead shade or heavy soil. Dwarf box (Buxus). Asarums. Lobelia syphilitica and maybe cardinalis. Salvia Black and Blue has tolerated a surprising amount of shade in my garden and blooms long.
Most perennials will not bloom for all that long so look for continued interest in contrasting form, texture and leaf color.

Bleeding hearts, hostas, astilbe and columbine are my favorites.