Okay, so the complicated answer:
You're all correct.
Cher/ch?re = dear.
Ch?ri/ch?rie = darling, love.
As soon as you put mon/ma in front of it, you say "my," or you're giving it possession. Your gentleman is correct that Ch?ri(e) is a noun and cher/ch?re is an adjective.
"Darling, could you hand me my purse please?" In this case, Darling represents your significant orther, and instead of naming them, you've given them a pet name. So that does fall into the person/place/thing category.
I think the confusion comes from the fact that in English, "dear" is both an adjective and a noun. The French use it as an adjective when it comes to applying "cher" to people. It is a quality of a person. They are...highly valued, emotionally, to us.
So, "ma ch?re" when it all gets broken down and examined is technically translated into "the person[noun] whom is important [adjective(dear)] to me."
I hope that helps.
V