Internal and External Blog

Can we have both a private company blog and a public blog with WordPress?

Yes, but it depends on how you define private. We use WP multisite subdomains. We have over 200 sites, most of them public. But we have a few sites that are “private” – requires user to login. Additionally the user has to have been registered with the site.

You can achieve this using a plugin. We wrote our own but there are many out there, for example – http://wordpress.org/support/plugin/private-only