Semi-transparent QWidget over QGLWidget: Strange results

I have a full size QGLWidget which paints the application background using QPainter (might change to native openGL commands in the future).

On top of this QGLWidget I use QWidgets (non-GL) for the user interface elements. These are, for example, QLineEdits and QPushButtons. I put them into a custom painted QWidget which uses semi-transparent background painting. The paintEvents of the QLineEdit and QPushButton are overwritten and use semi-transparent backgrounds, too.

The whole UI should look like the following (This is a screenshot where I disabled OpenGL and used QWidget instead of QGLWidget for the background. Note the semi-transparent top bar which also draws a shadow (within its own region)):

When the QLineEdit has the focus, it should have a higher opacity but still not fully opaque:

So now, with OpenGL enabled (The background then is a QGLWidget), the semi-transparent widgets above don't paint on top of the background but on (it seems to be) uninitialized data. The image shining through the top bar is sometimes the whole window itself and sometimes other windows currently being on my desktop.

This currently looks like the following (In this screenshot, the data on which the semi-transparent painting operations are painted on seems to be an image of the widget itself, having an offset.):

When I wrote text into the line edit (here: "This is some text which has been there before!"), removed it and set the focus back to the background widget (so the magnifier icon and the placeholder text appear), the previously painted things still shine through (Note that the visible border should not be visible anymore, but also still shines through):

So the problem is: Instead of being painted on top of the underlying widgets, the semi-transparent widget is painted on top of the old results, initially being something like "uninitialized memory".

Why does this happen? How can I solve the problem?

Things you should know before answering:

• The background scene is a composition of tiles which are rendered off-screen. So it can be painted very fast and repainting of the background for every little change of the overlay isn't problematic.
• The top bar is a custom QWidget with manual painting and arrangement of the contained two widgets (the button and line edit).
• The two widgets overwrite the paintEvent, only draw their own (semi-transparent) background when they have focus and don't use frames already provided by Qt. So the white border in the second screenshot is drawn in my custom paintEvent.
• I want the background and the composition of overlay widgets to be separately implementable. The background is an AbstractMapView which has some concrete map view classes. The whole window is an AbstractView (there are multiple concrete views, too), which contains both a concrete map view and the overlay widgets, composed in a way itself decides. Therefore, I don't want the logic of the overlay widgets to be part of the underlying map view. (I hope you understood this, as it is a bit complicated.)