Use of "between" with a "list" and a phrase

I want to use the word "between" to describe a relationship involving two concepts, but one of them itself consists of a list of two concepts. It's something like the following:

"We are studying the relationship between [cats and dogs] and the people who love them".

The idea "cats and dogs" is being related to "the people who love them"; there would be no brackets in the final sentence, but can it be presented like that? Does there need to be a comma after "dogs" to make the sentence clearer?

Thank you!