C.S.
Yes, mange is contagious. The two types of mange are demodectic and sarcoptic. The first is NOT contagious, but the second is. The mites will get into the skin of a human, but the immune system will not allow them to 'live' there. My understanding was that demodectic mange is somewhat of a genetic thing in dogs - perhaps it is the low immune system that is the genetic part, either way, I would take BOTH pets it, because if one pet got it then the other one may have it, and they will be passing it back and forth.
I got sarcoptic from my dog, we were very clean, but he picked it up from a neighbor dog :( I had a few bumps on my arm, they went away by themselves.