Two Blogs Sharing Elements

Is there a way to share elements from one blog to another?

I would like to set up two blogs on the same domain. One public and one private. Using the same theme.

And share some blog elements. Mainly I would like to have the navigation menu from the public blog to show on the private blog, in addition to the private blogs navigation menu.

Other possible elements, might be a calendar that is used across both blogs.

Having said all that, the only reason I need to do this, is that it is my understanding that you cannot both private and public pages on the same blog – it’s all or nothing. Correct?

Thanks in advance.