I first tried to "Separate Connected Surfaces" which created an inverted copy of the model. This might work if i try to print the model but I feel a bit worried because it's two models involved...?
Then I tried "Identify non-manifold edges" which seems to do the trick. There seems to be one single solid model.
Where can I find the option "Merge all shapes int a single solid model"?
Thanx for all your suggestions and explaining!