Surface reflections severely degrade the performance of the structured-light 3D measurement. In this article, we introduce a novel structured-light 3D measurement technique that works in the presence of reflective highlights. The focus of this article is on designing chessboard-like coding schema and crossover-based decoding schemes. First, we design chessboard-like fringe patterns that are resistant to reflective highlights by using simple logical operations. Compared with conventional coding schemes that inevitably have low-frequency patterns, the chessboard-like coding schemes use all-high-frequency patterns to provide a better highlights-suppression effect. Second, we propose an inverse-pattern method to extract crossover positions for decoding. The chessboard-like patterns have abundant crossover information. The crossover information is more localizable and better preserved than image intensity, which makes the decoding strategy more robust. Moreover, both positive and negative patterns are used to precisely localize the crossover positions. The proposed method can be readily incorporated into existing binary structured-light measurement techniques without significant overhead in terms of capture time or hardware. Extensive experiments are shown to demonstrate the high performance of the proposed method.