A modular system for continuously insulating exterior walls of a structure and cladding the structure walls provides thermally isolated MFI-brackets secured to a structural wall supporting thermally isolated vertical or horizontal rails supporting exterior cladding. Thermal insulation is positionally retained against the structure wall interior of the exterior cladding by the MFI-brackets and a pressure equalized moisture controlling rain screen is maintained between the interior surface of the exterior cladding and an exterior facing surface of the insulation.