Hi Peggy.
That is a very specialized question. I am not an expert in white dwarfs, but as your question has been up here for a few days I would guess nobody else on our panel is either, so I will say what I can.

I did a quick search of the astrophysical literature (using http://adsabs.harvard.edu/). It seems that there is hydrogen in white dwarfs, although not much. There seem to be various people modeling the details of how much hydrogen there should be and where. There are also references to the H-alpha line. I don't have time to do more research than that.

Cheers,
Terry