This research concentrates on the 2-D, steady, laminar, viscous, incompressible boundary layer flow of a biomagnetic fluid containing two different magnetic particles (CoFe2O4andFe3O4) over a continuously moving horizontal plate in the presence of a magnetic field generated by a magnetic dipole. For the mathematical formulation the comprehensive concept of Biomagnetic Fluid Dynamics (BFD) is adopted incorporating the principles of FerroHydroDynamics (FHD) and MagnetoHydroDynamics (MHD). The physical problem which is constituted by a coupled system of Partial Differential Equations (PDEs) along with corresponding boundary conditions, is transformed into a coupled system of nonlinear Ordinary Differential Equations (ODEs) subject to analogous boundary conditions by establishing newly simplified similarity transformations. The transformed ODEs along with the boundary conditions are then solved numerically by introducing an efficient numerical technique based on a finite difference algorithm. Verification of this work has been also done by comparing the obtained results with previously published results and found in quite good agreement. The significant effects caused by the variation of the governing parameters such as the skin friction, heat transfer rate and wall pressure are presented more intricately. It has been contemplated that including magnetic particles with pure blood enhances the impact of the magnetic field on the flow, temperature and pressure profiles which could be of interest engineering implementations, like, magnetic drug delivering in blood cells, separating RBCs (Red Blood Cells), controlling the flow of blood during surgeries, treating cancer by producing magnetic hyperthermia etc.