Unfortunately, we never got a good look at the interior of the “anniversary” waistcoat, but I think we can reasonably assume that there was a front facing, and that it was lined (although with what, we obviously can’t say).
Alex Murphy (aka “The Ginger Doctor”) and Daniel Pawlik claim the costumer who made the original waistcoat(s) told them that the waistcoats were underlined (“flatlined”) with lightweight hair canvas.
You can read his original blog post here:
https://thegingerdoctor.wordpress.com/2017/04/01/tipping-the-scales-eleventh-doctor-nirvana/
From this, I think we can reasonably assume that the “anniversary” waistcoat was similarly interfaced – and indeed, we can occasionally see what appears to be little strands of hair canvas poking through some of the buttonholes.