AbstractComputer‐aided design (CAD) models of industrial design are often plagued with a series of defects, including minute features, gaps, self‐intersections, and misalignments. The development of schemes in automatic defeaturing, gaps repairing, and intersection removal usually requires a discrete representation of the geometry. However, existing surface meshing methods could not effectively handle sliver surfaces and assemblies with complex contact conditions, including multiple misaligned curves/surfaces and degenerated or free‐form‐shaped interface of contact. A surface meshing method based on a meshing‐and‐synchronizing strategy is proposed, which tackles the mesh generation of sliver surfaces and the cleanup of misaligned assemblies by means of mesh alignment. The mesh generation is performed in a hierarchical manner with curves and surfaces being meshed in sequence. By incorporating the synchronization strategy into the curve/surface meshing process, curve/surface mesh alignment is achieved automatically without compromising the mesh quality. Thanks to the alignment, the curve mesh generated by aligned curve meshing (ACM) is free of intersections, which enhances the meshing of sliver surfaces. By enforcing mesh alignment, aligned surface meshing (ASM) can handle misaligned assemblies with complex contact conditions. ASM is parallelized by using OpenMP. Various assemblies characterized with difficult misaligned features and touches are well processed by parallel ASM.