Cached post for logged in user

I want to cache my site’s HTML, not just static, so basically to cache everything, but I don’t want to cache HTML for logged users, so if a users logged in and viewing posts, its HTML is fresh each time and won’t be cached. Is it possible?

In the past I used CF with cache everything, though I already add exception for admin and preview, but when I visited newly posted article, and later try to open that post as regular visitor, I could see the admin bar because the cache created when I visiting it as logged user.