Method of improving humidity resistance in a coated article (19) comprising a carbon-carbon composite component (10), a graphite component (10), or a ceramic matrix composite component based on carbon fibers and/or graphite (10). The component (10) is preferably configured as an aircraft landing system brake disc. The method includes the steps of: (A) providing a carbon-carbon composite component (10), a graphite component (10), or a ceramic matrix composite component based on carbon fibers and/or graphite (10); (B) covering the component (10) with a phosphorus-containing antioxidant undercoating (11) having a thickness of approximately 1 10 mil; and (C) covering the resulting undercoated component (10, 11) with a boron-containing glass overcoating (12) having a thickness of approximately 1 10 mil. The overcoating includes 20 50 wt-% alkali or alkaline earth metal silicates, 3 25 wt-% alkali metal hydroxide, up to 10 wt-% boron nitride, and one or both of 5 40 wt-% elemental boron and 5 40 wt-% boron carbide. The overcoating is substantially free of phosphoric acid and phosphates. Also, articles coated with the specified undercoating/overcoating combinations.