Culinary herbs to grow under black pine and walnut?

Which herbs would grow best in partial shade between black pine and a carpathian walnut?  There are lots of roots near the surface, but I think they're all pine. It is well drained and will be dry because of competition from tree roots. I'm looking mostly for a ground cover but of some use. I can't use medicinal herbs because of a kidney problem.

For a ground cover, look at thyme.  I was planning to use creeping thyme as it is very low growing and lovely to look at but I was told it was hard to grow from seed.  

Also what about lemon balm?  It is not as invasive as other mints since it does not have rhizomes.