The google definition of this word states that it is a noun however in its own example of usage it is used as an adjective: "a frail, milquetoast character". I haven't found any reliable sources to say that it can be used as an adjective so I'm wondering if it would actually be correct to use this word as an adjective.
The term milquetoast is a noun
a person who is timid or submissive
In the example you give, it is still a noun, but it is used adjectivally, as many nouns can be.
I shut the barn door.
I wrote a computer program.
My kitchen floor is dirty.
These are sometimes called attributive nouns or noun adjuncts