I don't get this joke from Modern Family (City mouse/country mice)
Cam: Mitchell is a snob.
Mitchell: No, I'm just discerning.
Cam: Official slogan for snobs.
When we first met, he wouldn't even look at me because I was a hick from the farm in Missouri, and he's a big **city mouse**.
Mitchell: (snorts) Who says city mouse?
Cam: **Country mice.**
I don't get this city mouse / country mice joke. I know the meaning of every vocabulary here but I guess there's more to it cause I just don't get this conversation when it's taken literally. What's supposed to be funny in this context? Is "city mouse" or similar phrase of this sort a common joke in English?
Thanks in advance!