"Confuse A & B" vs. "Confuse between A & B"

As a native speaker of American English, I would say that someone "confused A with B."

I might also say, on the other hand, that "there was some confusion on [someone]'s part between A and B."

Notice that when I use between, it does not immediately follow the verb (or verb phrase) as in your example. That is because the word between, a preposition introducing a prepositional phrase, does not function well as a direct object. Instead, it functions as an adjective modifying the noun confusion.

If you want a direct object to follow the verb confused, my first example works better, being more concise.