Today I decided to tackle the problem of needing public and private files. Again.
At the first attempt I switched the default download method in admin/config/media/file-system from 'public' to 'private'. From that moment on, no picture was visible any more. After many hours of digging around, I gave up and switched the download method back to public.
Later I found that all pictures needed to be referenced in the database with a 'public://' or a 'private://' prefix.
With the move from IMCEImage to FileField, this was fixed.