"have as"

(Grammar Questions I Couldn't Answer)

One of my students had a question about the vocabulary homework I had assigned him.  (Unit 2 Vocabulary, p.125 from Complete IELTS Bands 6.5-7.5).

The book defined the word "comprise" as follows:

comprise: v [T] to have as parts or members, or to be those parts or members

The student couldn't understand the meaning of "have as", and thought a mistake had been made in the printing of the book.
I assured him no mistake had been made, and tried to explain it.

I assumed his confusion was with "as" following "have".  As an ESL student, I assumed he had learned that "have" was a verb that always took an object--e.g. "I have a dog".
I explained to him that we can also use "have as" to explain the nature of the relationship.  For example: "I have her as an employee" would be different than "I have her as a boss."

My student pointed out to me, however, that in both of my examples there was still an object between "have" and "as".
Why was there no object in the sentence he was questioning me about?  Shouldn't it be "to have something as parts or members"  ?

I was unable to give him a satisfactory answer.