He is smarter than the pair of us.
The sentence is from a British parent who is talking about their son and means he is smarter than both of his parents.
I focused on "the pair of us" in the sentence, and wondered if it could be a synonym of "both of us". I have looked up but it does not seem to be common.
My question is: Is "both of us" and "the pair of us" interchangeable?
No, they’re not interchangeable.
The use of "the pair" suggests that the two are a single unit, as parents often consider themselves. Using "both" instead removes this meaning, so the two are not identical.
Both are grammatically correct and natural.