I had assumed that lips sat "on top" of face textures, but I guess I was wrong...

I find that Antonia's lip transition is a bit "harsh," so I created a transparency map with soft edges around the lips, which I assumed would "bleed" into the facial skin. Instead the bleed area previews as white, and renders as black.

What is the proper procedure?

For the time being, I'm faking things in the texture itself by putting facial skin on a layer below the lips and doing a semi-transparent erase around the edges. It's an improvement, but the problem is that if you want a different shader on the lips than on the skin (usually, I'd say), you can see the difference.

I've had a problem with this as well, not just on Antonia.

For Antonia I find that when I use a natural lip color and on the face map with a little skin color surrounding the lips, it works very well.

But when I change lip color I get the white edge around the lips.

I'm still working on it and if I succeed in doing it right, I'll post how I did it.

Or we could maybe get Robynsveil or Saintfox to share their technique. :)

If you get white around a seam it's usually due to texture filtering.  Adjusting or removing it entirely should fix the problem.

I almost always have texture filtering set to "None," although on rare occasions I'm now using the new "Crisp" for certain zones.