I mulched around rhodos with a thin layer of newspaper topped with about two inches of wood chips I got free from an arborist and it worked. I would not mulch rhodos much deeper than that. I can't say exactly why but I would be hesitant to use rock mulch on rhodos - maybe because I've never seen it and that's not what they get in the wild. Leaves and pine needles also make a good mulch for rhodos. FYI, don't let the baby chew on rhodos or azaleas. Don't use English Ivy as a ground cover as it will overtake your other plants. I do have some sort of wild strawberry (not necessarily edible, I don't know) volunteering under some rhodos and azaleas and they seem to coexist nicely.

Rhododendrons native habitat is as understory plants in the forest where they grow quite happily in a soil well endowed with organic matter. You could quite easily lay down some newspaper ofer the soil and cover that with some wood chips you got, free, from one of your local tree cutters (I hesitate to use the term Arborist since many are not). I too have wild strawberries growing around my Rhododendrons and Azaleas and the fruit the produce is much better tasting than the cultivated strawberries I also grow.