I think "is" is correct. See this example: "One of them **is** going to win the prize" However, in spoken English many native speakers would one or both of the options and only an unfriendly person would interrupt the flow of conversation to correct such a small thing...in my opinion ;)

Technically, "either" is singular. You can think of it as "either one". So, formally, you should use "either of them is home". But informally and in conversation, you'll hear "either of them are". Preferably, you should know that "either is" is correct but still understand it when people say "either are".