Sometimes, and a private persona with close family and friends.

One solution is to create two separate Facebook accounts, but this requires... managing two separate Facebook accounts. Another solution is to use your private Facebook account to create a page for your public persona. You can then continue to interact with your close family and friends via the private persona, and interact with everything else via the public page.

But what happens when the public-facing part of your persona wants to interact in non-public ways on Facebook? For instance, what if a priest wants to join a temporary, private Facebook group for members of his parish going on a pilgrimage with him?

Jeff Moore and I investigated this, and the results of our experiments are as follows:

  1. The "private persona" -- that is, one's normal account -- continues to be a normal account; it can join private/secret groups, post on the personal profiles of friends, and so forth.
  2. The "public persona" -- that is, the page -- can be followed (in lieu of being friended) and send/receive messages as if it were a separate account. Cool! This resolves the vast majority of use-cases.
  3. The "public persona" can create public events, and converse with others inside that event using the public persona. (screenshot below: Jeff's public event for his diaconate ordination, hosted by his public persona, which is a Facebook page. Jeff is commenting under his public persona within the event, and the drop-down indicator for choosing between private/public personas is circled.)
    jeff-publicoption
  4. However, the "public persona" cannot join a group, regardless of whether it is open, closed, or secret, and regardless of whether the "private persona" is a member of that group. (screenshot below: Jeff's UI for a Facebook group, with no option to choose between public and private personas; the space that used to be the drop-down indicator for choosing between private/public personas is circled -- note that the image is a bit confusing because it includes the previous image within it... pay attention to the bottom right circle, because th other circle is a screen capture.)
    jeff-nopublicoption
  5. For what it's worth, the "public persona" also cannot post on the personal pages of other accounts.

To summarize: Pages appear to be built for others to interact with, not built to interact with others. Public personas built as pages within personal/private accounts allow for private messaging as the private persona, but do not allow for group interaction, private or not. If you need to have specific group interactions, especially private group interactions, as your public persona, you need to use something other than Facebook.

This is the best we can tell based on limited experiments. Experiments were a joint effort between myself and Jeff; the writeup (and any errors in it) are mine alone. Corrections, addendums, etc. are absolutely welcome!