This paper addresses a fundamental challenge in 3D medical image processing: how to deal with imaging thickness. For anisotropic medical volumes, there is a significant performance gap between thin-slice (mostly 1mm) and thick-slice (mostly 5mm) volumes. Prior arts tend to use 3D approaches for the thin-slice and 2D approaches for the thick-slice, respectively. We aim at a unified approach for both thin- and thick-slice medical volumes. Inspired by recent advances in video analysis, we propose AlignShift, a novel parameter-free operator to convert theoretically any 2D pretrained network into thickness-aware 3D network. Remarkably, the converted networks behave like 3D for the thin-slice, nevertheless degenerate to 2D for the thick-slice adaptively. The unified thickness-aware representation learning is achieved by shifting and fusing aligned "virtual slices" as per the input imaging thickness. Extensive experiments on public large-scale DeepLesion benchmark, consisting of 32K lesions for universal lesion detection, validate the effectiveness of our method, which outperforms previous state of the art by considerable margins without whistles and bells. More importantly, to our knowledge, this is the first method that bridges the performance gap between thin- and thick-slice volumes by a unified framework. To improve research reproducibility, our code in PyTorch is open source at https://github.com/M3DV/AlignShift.