A system for supporting exterior panels on a substrate of a building structure. The system has a plurality of polymeric bracket members, and each of the bracket members have at least one anchor section, at least one web section and at least one support section. The polymeric bracket members provide a thermal break from the exterior panel to the substrate of the building structure. A plurality of exterior cladding units are held in place by the bracket members. A plurality of vents are disposed between the panels and the exterior panels, and a plurality of vents are also disposed between the panels and the substrate, thereby forming a ventilation system.