Mucus is a noun meaning the viscous, slippery substance secreted as a protective lubricant coating cells and glands of the mucous membranes. Mucous is an adjective meaning (1) containing, producing, or secreting mucus or (2) relating to, consisting of, or resembling mucus.
In the phrase mucous membrane, mucous is correct because it is an adjective modifying membrane.
Examples
Misuse of the adjective mucous in place of the noun mucus is common—for example:
For example, mucous may plug sinus passages or the tube between the nose and ear … [Patch]
One tipoff that this has happened is when mucous turns yellow, green or brown. [San Antonio Express]
These writers use mucus correctly:
The tableware, the color of mucus and as bendable as a pocket watch in a Salvador Dali painting … [Fox News]
Between 0.5 and 5 mm, they live off the skin, blood and mucus of the host salmon. [Mayo News]
And these writers use mucous well:
The warm water felt good against his cold mucous skin. [Village]
The syndrome is a rare, life-threatening disorder in which the skin and mucous membranes react severely to a medication or infection … [Minneapolis Star Tribune]

