free probability provides a unifying framework for studying random multi-matrix models in the large $n$ limit. typically, the purview of these techniques is limited to invariant or mean-field ensembles. nevertheless, we show that random band matrices fit quite naturally into this framework. our considerations extend to the infinitesimal level, where finer results can be stated for the $\frac{1}{n}$ correction. as an application, we consider the question of outliers for finite-rank perturbations of our model. in particular, we find outliers at the classical positions from the deformed wigner ensemble. no background in free probability is assumed.