Blogs are tipically public content mediums, so I would reflect if a blog is the best solution for your family closed content.
An excellent blog post can take hours to write and most family members generally will not want to spend so much time producing content for a small, although important, audience. Another problem is that due to the semi-professional and public nature of blogs, blog engines require some learning to use properly, and your family members may not want to spend time doing it.
What solutions for a family project?
I would suggest other forms of presenting content such as a microblog. status.net is an open source php script that you can use to create your private microblog (or public microblog), limiting posts to 140 characters or any other number you want. To see what status.net can do, I would suggest to look at the public http://identi.ca/ as an example of a status.net blog.
The easiest solution is to use one of the existing social networks. Many of your family members may already have a Facebook account and are used to Facebook user interface, so you can create a Facebook closed group.
Other options are a mail-list, a forum or a private photo gallery.
I also agree with Bevan above on Drupal. But Drupal is a professional content management system for professional websites. Because it's so flexible, you will have to spend a lot of time configuring it for this purpose.