Q. My understanding is that the word family is a noun or adjective. So if you use it in a sentence like “We ordered a family-sized pizza for the party,” is the hyphen used correctly in this instance despite the fact family ends in ly?
A. When CMOS 5.93 says “A two-word phrasal adjective that begins with an adverb ending in -ly is not hyphenated,” it’s referring to adverbs (not nouns or adjectives) where -ly is added to a root word: slyly, gladly. Words like ply, homily, and family happen to end in -ly, but the -ly is not an ending; it’s part of the word. And they aren’t adverbs. The section of the hyphenation table (CMOS 7.89) that you’re looking for is “noun + participle” (family + sized), where you will see that the hyphen is correct.