For clarification: I have 2 reports in my Composite, the problem was that they were shown above eachother even though I had them in different bands. They were actually drawn wrong.
After some experimentation I found out it was the way I populated the reports. I populate them at the same time within a for-loop. I made the guess that the Composite then can't figure where the first one ends so the other one can start. I've made composites with SQL-reports before, this error can't occur then.
The solution was to populate the report at the top first, and at the same time add data to a temporary datastore. When I was done looping, I copied the data from the datastore to the report at the bottom of the Composite and that gave me the desired effect.