custom header top

I didn't find anything about this, maybe not possible:

Can you move the custom header code above the menu bar in the layout (without editing the html)?
With custom header I mean the "header" file that's available in he page editor.

So in the attached screenshot example: have the yellow part above the grey menu bar.
In my case the custom header would be a smal height bar the covers the entire width of the page, it should be always there on all pages.

Thanks