This invention relates to building materials and methods. A building assembly for constructing a building includes load bearing structural panels joined and finished with a non-load bearing panels. The load bearing panels comprise a structural concrete insulating panel (SCIP) comprising a pair of wire mesh members sandwiching a middle member comprising polystyrene, wherein each of said wire mesh members defines two outwardly projecting screed ridges. The non-load bearing panels comprise a pair of fiber cement boards sandwiching a polystyrene core. The load bearing SCIP panel is placed in position and then the non-load bearing panel is positioned in a desirous location abutting the SCIP. The SCIP then receives a layer of cementitious material that is cut flat using the screed ridges. The assembled SCIP and non-load bearing composite is then finished with a final finishing layer so that the entire assembly has the same outer appearance.