Originally Posted by
Flying Lawyer
Being a foreigner with a reasonable command of English I would certainly understand, that both, the parking and the valet service is for free. "Valet" is a noun and "parking" is a noun and to my understanding the adjective "free" refers to both nouns. Otherwise I would expect a "Parking with free valet service"
Actually valet is used as an adjective describing the type of parking. Since the word parking is the only noun, complimentary, an adjective, should apply to that word.