Accurate dosimetry and determination of the biological effectiveness of boron neutron capture therapy (BNCT) is challenging because of the mix of different types and energies of radiation at the cellular and subcellular levels. In this paper, we present a computational, multiscale system of models to better assess the relative biological effectiveness (RBE) and compound biological effectiveness (CBE) of several neutron sources as applied to BNCT using boronophenylalanine (BPA) and a potential monoclonal antibody (mAb) that targets HER-2-positive cells with Trastuzumab. The multiscale model is tested against published in vitro and in vivo measurements of cell survival with and without boron. The combined dosimetric and radiobiological model includes an analytical formulation that accounts for the type of neutron source, the tissue- or cancer-specific dose-response characteristics, and the microdistribution of boron. Tests of the model against results from published experiments with and without boron show good agreement between modeled and experimentally determined cell survival for neutrons alone and in combination with boron. The system of models developed in this work is potentially useful as an aid for the optimization and individualization of BNCT for HER-2-positive cancers, as well as other cancers, that can be targeted with mAb or a conventional BPA compound.