A word is said to be bordered if it contains a nonempty proper prefix that is also a suffix. A pair of words (u, v) is said to be mutually bordered if there exists a word that is a nonempty proper prefix of u and suffix of v, and there exists a word that is a nonempty proper suffix of u and prefix of v. Recently, Gabric studied the number of mutually bordered pairs. In this work, we extend the concept of mutually bordered pairs to abelian setting, and determine the number of mutually abelian-bordered pairs of binary words using lattice paths. We also find the number of unbordered pairs in this context.