And Catholic in Catholic junior high school tells us what kind of junior high school it is. But is Catholic junior high school another compound noun?
The interesting and frustrating thing for me about word classes and labels is that there are no indisputably correct answers. A mammologist may be able to tell us whether mammal A is a sheep or a goat, and a lepidopterist may be able to tell us where insect B is a butterfly or a moth, and be reasonably certain that fellow mammologists/lepidopterists will agree. Some grammarians, however, spend half their professional lives arguing about labels. In my lifetime I have seen articles expelled from the adjective class, determiners (or determinatives) come into existence and, for some grammarians, many adverbs become prepositions. I shall doubtless live to see a few more changes.
My personal view (and that's all it can be) is that such expressions as
high school, grammar school, primary school, etc, are compound nouns. The first word of each pair may well have begun life as an adjective (like the 'black' in 'blackboard) but has become over time part of a single compound noun, despite the fact that that noun is written as two separate words. I feel that, in British English at least,
state school, public school, and even
private school are also compound nouns.
I feel the same about
junior high school.
I am, at the moment, not sure how I feel about
Catholic junior high school or
single-sex grammar school. The words in bold seem to me to be more like noun modifiers than parts of compound nouns, but I can't think of a convincing justification for this.