Insulation panels for wall construction and roofing installation are characterized by inlaid battens in outer faces thereof by which multiple layers of insulation can be installed without thermal bridging. Second and any subsequent layers are each fastened only to the battens of the immediately underlying layer, without fully penetrating therethrough to the roof deck, building wrap or other substrate. Laminated facers of perforated character allow migration of moisture to and from a foam core of the panel, while internal channels and internal slots beneath the facer enable drainage/drying of excess moisture without material degradation of the inlaid battens. Additional drainage space within each layer is provided at inter-panel connections, where tongue and groove connections are configured to leave such drainage space open between the tongue and groove.