Java: Making a window click-through (including text/images)

I want to create an overlay in Java that is transparent, always on top, and that I can click-through. I've found some similar posts about this issue, but even after following their answers, I'm having one issue.

My problem is making the whole window click-through. I'm not having any problem making it work with a JFrame, but once I add any components to it (JLabel or an ImagePanel), the click-through attribute doesn't carry over to them.

As I want to have a background image for my application this basically makes the code I have useless seeing how the window gets focused whenever I click the area the text/image covers.

Before I show the code I'm using I'd first like to refer to these threads which essentially describes precisely what I want, except in C#.

My goal is to create an overlay with a transparent .png-image and some text on-top that will change on key events. If it uses JFrame or any other library doesn't matter. I only need it compatible with Windows.

I'd also like to mention that I've got some experience with Java, but am a novice in using JFrame.

import java.awt.BorderLayout;

import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.SwingConstants;

import com.sun.jna.platform.WindowUtils;


public class Overlay {
    public static void main(String[] args) {
        JFrame frame = new JFrame("Overlay Window");
        frame.setUndecorated(true);
        frame.s