Of course, because both groups view themselves as belonging to the same group of people, with shared customs, history, religion and tradition, that dates back to the Kingdom of Israel. What you don't seem to understand is that ethnicity is a social concept - the criteria isn't "how much two people have in common", but whether a shared identity exists between them. You should ask yourself what makes you refer to both Ashkenazim and Mizrahim as "Jews", and what makes them refer to themselves as such, even among people who don't believe in Judaism.
> Well, Italians and Spaniards traditionally share a religion (Roman Catholicism), speak related languages, and share some biological ancestry – does that make them one ethnic group?
If they share the same ethnic identity then of course.