I've seen no evidence for something specialized worn under mail in the 15th Century. But it's near certainly more than just a shirt. I'm thinking it's assumed that the guy wears a doublet. You almost never see anyone in just a shirt, unless it's some beggar or allegorical painting where the shirted/naked person is getting abused or somesuch. If you look at Schilling or Beachamp battle scenes, the pedestrians with brigs and maile (I presume full maile shirts under the brigs) have full-length, tight-fitting sleeves - consistant with some sort of doublet. It doesn't LOOK padded or anything special through the arms. It's quite possibly their daily-wear doublet. That your above quote DOESN'T mention a specialized piece of garb under the maile lends credence to the "nothing special" theory. Question is; did they, or do YOU want to get your good doublet "besmotred by your Habergeon"? Because as ya know, maile is dirty and stresses what's worn under it.
Conversely, in the (14th C.) Chaucer passage in the "Knight's Tale" I took the above quote from, the squire is wearing his stained gear while traveling, so while it IS dicussed as a specialized item, it is also being treated as daily wear.
Me, I'd wear a lightly-padded linen-covered arming doublet, and save my good wool doublet from the mess. (but I'm fussy)
--------------------
Geoffrey Bourrette
Man At Arms