The mites that cats can get are mange and are orange.
Lice egg casings are white and are tiny like you said, but I don't think you would see them moving, since they are empty. Could your eyes be playing tricks on you? The nice thing is that a good flea bathe should take care of them.
If it's possible a vet check might be a good idea, since if they are a cat parasite it can be serious in kittens.
My only other thought is: could there be bugs in their food etc., maybe something is just hopping a ride. I think that's unlikely though, if you are seeing so many.
How old are your kittens? If you give them a flea bath, or treat them with anything that kills parasites, it could kill the kittens. Be very careful----I didn't know this, and I gave a flea bath to a kitten I had gotten for my son-----I didn't want to do it, but it had fleas bad, and that can cause them to become anemic. Well, the kitten died before I even got to work the next morning. I've never felt so horrible about a pet's demise, as I caused it. I think you should probably get a vet's advice asap-----kittens can go downhill quickly.