For "to be" as an intransitive verb.

For "to be" as an intransitive verb.

First, please look at this sentence.

"The financial health of the company is in doubt."

Couldn't someone answer me whether or not this prepositional phrase of "in doubt" is a kind of "adjective phrase" or "adverbial phrase" ?
I've definitely thought it is an adverbial phrase, because the "to be" is being conducted as a role of "intransitive verb",not of "linking verb". Am I not right ?
But someone is very terribly and continuously insisting that that one, "in doubt" is an adjective phrase in the sentence.Even though I have put out some example sentences like these, "This book is on the desk", "This job is among well paying one in the industry" and so on, It is still the same. His answer is only that the meaning of "in doubt" indicates "not certain" in the dictionary he keeps now, that's why it should be treated as an adjective phrase.
How could he forget that the word of "not" is an adverb of "not certain"!
Ah~, could you confirm whether it is an adjective phrase or adverbial phrase