Any hints how to avoid it?
The header was made in the master and can't be seen as a layer on the site-edit page...
In your case, I guess, it should do the job, when you …:
… put all header elements into one layer and have this layer on top in your layers palette
AND on your page/pages put content in another layer, which is below the top layer in layers palette.
In your case – do not put anything of your content in the same layer as the header elements from master.
the scroll bar makes me think you have a cms (blog?) div sitting in there somewhere as well