We study strategies to interface finite-difference time-domain (FDTD) update equations in heterogeneous structured grid components for overset composite FDTD grids. An overset composite grid (or “chimera” grid) is a heterogeneous grid formed by the combination of structured FDTD subgrid components chosen to better conform to local geometrical features. We study the performance of various analytical filters and phase matching techniques to reduce problems associated with such heterogeneous grid interfacing, including spatial frequency aliasing and (numerical) phase velocity mismatch. We demonstrate the performance of interfacing algorithms in some canonical examples.