Discussion-based email list from WP users?

I have what seems like a simple idea but is proving difficult to implement.

I want an email list solution that automatically includes my users’ email addresses (my site is closed to registration) and lets them post to it. The idea is that the site automatically acts as a LISTSERV for my user base, so they can all email uniquelist@mysite.com and it will automatically send a copy of their message to all other users.

There are a number of email list options out there, and some have WP integration, but they are virtually all oriented towards subscriptions to a newsletter, or something that the admin only can post to. That’s not at all what I need – I need an internal discussion system.

Any suggestions at all? I’d even be willing to write a basic script myself if I knew anything about passing received emails to a script. Advice of any kind would be appreciated here, even if you (like me) are not sure how to accomplish the entire system.