JasperReports - Splitting a band's background

Question

Though my company's system creates the reports dynamically, I could manually reduce my scenario to this:
- Two details bands, with a bunch of static texts in them;
- A frame object in the second band, so I can create a background filling the whole band;

My main problem: when the second band reaches de end of the page and breaks to the next one, the background frame is printed in it's whole height. A sample screenshot:

As you can see, the band's beginning doesn't print the frame (because of it's height) and it is printed with his whole height in the second page, pushing the second text label down. That is basically my problem: the frame background pushes the text of the bands that overflow the page.

I've played a lot with the properties, and nothing yet. For the band, I'm using Stretch split type (and tried Immediate); for the frame, I tried combining Print When Detail Overflows with Print Repeated Values, changed the height and Stretch Type to Relative to Band Height or Relative to Tallest Object. Nothing yet.

PS: Due to the dynamic nature of the software, using Float position type is not an option, since we must offer the option of setting the text's Top property to the client.

I'll be really thankful if someone has any idea if this is even possible with JasperReports.