Take a look at JLayeredPanes. Here is a tutorial.
edit:
If panelA is an AWT component, you will be hard pressed to get panelB to overlap. From Sun's article entitled Mixing Heavy and Light Components:
Do not mix lightweight (Swing) and heavyweight (AWT) components within a container where the lightweight component is expected to overlap the heavyweight one.
However, if you are looking to have panelA fill the Frame completely, why not add panelB as a component of panelA?
Edit2:
If you can make panelB a heavyweight component, then you can use the JLayeredPane.
Here is a quick mockup that shows how:
public static void main(String[] args){
new GUITest();
}
public GUITest() {
frame = new JFrame("test");
frame.setSize(300,300);
addStuffToFrame();
SwingUtilities.invokeLater(new Runnable(){
public void run() {
frame.setVisible(true);
}
});
}
private void addStuffToFrame() {
Panel awtPanel = new Panel();
awtPanel.setBackground(Color.blue);
//here you can fool around with the pane:
//first, you can see how the layered pane works by switching the
//DEFUALT_LAYER and PALLETTE_LAYER back and forth between the two panels
//and re-compiling to see the results
awtPanel.setSize(200,300);
frame.getLayeredPane().add(awtPanel, JLayeredPane.DEFAULT_LAYER);
//next you comment out the above two lines and
//uncomment the following line. this will give you the desired effect of
//awtPanel filling in the entire frame, even on a resize.
//frame.add(awtPanel);
Panel awtPanel2 = new Panel();
awtPanel2.setBackground(Color.red);
awtPanel2.setSize(300,200);
frame.getLayeredPane().add(awtPanel2,JLayeredPane.PALETTE_LAYER);
}