Full-wave modeling of 3-D doubly periodic structures with non-orthogonal lattices is an important topic area in computational electromagnetics due to its wide range of possible applications; most notably, frequency selective surfaces (FSS) and metamaterials. The hybrid finite element boundary integral (FEBI) method has been used to analyze the "artificial puck plate" FSS using a triangular grid composed of isotropic media . Recent advances in artificially engineered materials requires implementation of complex and inhomogeneous media in device designs; one example being the use of anisotropic liquid crystals for tunable optical negative-index metamaterials . While many efficient simulation tools exist for doubly periodic structures with rectangular lattices, there has been little investigation into the modeling of similar structures which possess non-orthogonal lattices and inhomogeneous anisotropic materials. Here, these issues have been addressed with the development of a fast and efficient simulation tool which takes advantage of the adaptive integral method (AIM) . In this new code, triangular prism finite elements are employed to mesh the unit cell volume of the periodic structure, resulting in a great deal of flexibility in modeling complex geometries in the transverse direction (e.g. for modeling FSS screens with arbitrarily shaped elements). Additionally, the O(N·logN) FFT-based AIM is employed to accelerate the calculation of the matrix-vector product in the BI part of the bi-conjugate gradient (BCG) solver. Through several examples and a comparison to the original FEBI algorithm, the efficiency of the proposed technique is demonstrated and its results are validated.