I doubt if that is possible. The primary reason why I say so is because wordpress stores all the permalinks in the database. If you have a post with permalinks http://www.example.com/2010/08/post1, then you cannot have a 2nd blog which has a different URL to show the same post.
A manual way of doing this would be to copy the database over and then changing the permalinks for all the posts. It would have been more convenient if wordpress stored relative links as well... but then I wonder how search engines would be crawling through the posts!
Anyways, I'm trying to do something similar. I don't want to create exact replicas, but I do want some overlap in the posts that I publish on one blog to appear on the other and vice versa..
A checkbox plugin which lists the 2 blogs and in the backend stores data accordingly would help.. but it might get very complex as its not just posts.. we have tags, categories, comments and lots more!
A simple example of post sharing can been seen in gizmodo and lifehacker (and all their other blogs). I wonder if they simply copy and paste things or is there an automated way of doing such things.