Lice are species specific. Human lice will not infect goats, nor will goat lice infect humans. But you will need to start an appropriate course of treatment for your goats if you have not done so already.
Ivermectin orally or a pyrethrin dust topically are the best I've found.
The ivomec you want to treat, then treat again in 10-14 days to get the new hatch.
The dust, once a week for 3 weeks should clear up everything.
And I don't know, but I would imagine they can host both at the same time.... treatment is the same, so it really doesn't matter.
we use sevin dust on everything, works great and you dont have to even try and figure out for sure what it is, lice, mites, what type, sevin kills them all.