1. Layer > Flatten Image
2. Image > Mode > Grayscale
3. Layer > New > Layer From Background
4. Select > Load Selection (set channel to "Background Gray" and check "Invert")
5. Now you should have the running ants across the edges of your lineart, that is, all the black pixels should become "selected".
6. While you have the selection: Layer > New Fill Layer > Solid Color (select black color)
7. After you created the fill layer, the selection should be gone, now run Layer > New Fill Layer > Solid Color (with white color)
8. Drag the "white" layer under the "black" layer.
9. Delete "Layer 0" as you won't need it anymore.
10. Image > Mode > RGB
In the end you should get a picture identical to your original lineart, but with all the black lines separated from the white background, so you can insert color-layers under the black lines but above the white background. Personally, I've just recorded an "action" that runs all the commands above automatically.