This paper presents a multicomponent topology optimization method for designing structures assembled from additively-manufactured components, considering anisotropic material behavior for each component due to its build orientation and distinct material behavior and stress constraint at component interfaces (i.e., joints). Based upon the multicomponent topology optimization (MTO) framework, the simultaneous optimization of structural topology, its partitioning, and the build orientations of each component is achieved that maximizes an assembly-level structural stiffness performance, subject to a maximum stress constraint at component interfaces. The build orientations of each component are modeled by its orientation tensor that avoids numerical instability often experienced by the angular representation. A new joint model is introduced at component interfaces, which enables identifying the interface region, assigning a distinct tensor for the region, and imposing a maximum stress constraint in the region during optimization. Both 2D and 3D numerical examples are presented to illustrate the effect of the build orientation anisotropy and the component interface behavior on the resulting multicomponent assemblies. The example 3D assembly, optimized for a multi-load condition, is fabricated for the purpose of demonstration.