There are a few ways to approach this.

One way would be to set the Layer Mode of the layer you're coloring to Multiply.



Setting the layer mode to multiply,
lets the black lines show through.
However,
this may cause issues later on during the coloring process.
When other layers with color are added.



Another method would be to apply Color to Alpha on the white of the image.
This will remove all the white from the image.
Leaving the black lines on a transparent layer.

The first thing I would do if useing this method.
Would be to make sure that the white is indeed as close to white as it can be.

This can be done by using Color Curves.

In the example image below.
You can see that the white has some grays/dark pixels.


By using Color Curves,
this can be adjusted.


Then you can apply the Color to Alpha of the white.