We investigated the magnetotransport properties of high-mobility InAs/GaSb antidot lattices. For samples with large antidot diameter, we found a broad maximum of classical origin around 2.5 T in addition to the usual commensurability features at low magnetic fields. The broad maximum can be ascribed to a class of orbits involving multiple reflections on a single antidot. This is shown by both a simple transport calculation based on a classical Kubo formula and an analysis of the Poincaré sections at different magnetic-field values. At low temperatures we observe weak 1/B- periodic oscillations superimposed on the classical maximum.