I am the webmaster for a school that uses Google Apps for Your Domain, so every family has an account at our domain. We would like to create a blog that can only be read by school families. Blogger appears not to support this feature. (We would have to add everyone in the domain individually.) Is there another free (or cheap) blog service that offers this functionality, including using Google authentication (i.e., not requiring people to create another password)?
You are correct, Blogger does not support this feature.
Google Sites lets you create a website that is restricted to people who have access to the domain.
If you use a "News" (I think that's the right one) type of page, it effectively creates a blog-style site which you can make posts to. (And the post-editor appears to be based on the same tools as the Blogger post-editor.
There may be an issue, though, be about the long-term plan for Sites. My perception is that it's not been widely adopted, so it's possible that Google may stop providing it.
I don't know if any other service could make it easier for you than Blogger. keep in mind that with any service, in order to do what want, you have to define/invite each user individually.
With Blogger you can do this very easily, you just have to invite all your readers to your blog, and as long as they all have Google accounts, they don't need to create any new accounts for blogger. see this for more information: Blog Readers: Control permissions