Obviously, because of the waistcoat’s lapels, we know that the 11th Doctor’s velvet waistcoat had a front facing made of the same velvet as the front of the waistcoat.
Alex Murphy (aka “The Ginger Doctor”) and Daniel Pawlik also claim the original costumer told them that the waistcoats were underlined (“flatlined”) with lightweight hair canvas.
You can read his original blog post here:
In a couple publicity photos, we can see what appears to be some hair canvas poking through one of the buttonholes.
Unfortunately, I wasn’t able to determine what color the waistcoat lining was … only that, unlike the “scales” waistcoat, it wasn’t a lighter white/off-white, but definitely a dark color.