Structured illumination microscopy (SIM) doubles the spatial resolution of a fluorescence microscope without requiring high laser powers or specialized fluorophores. However, the excitation of out-of-focus fluorescence can accelerate photobleaching and phototoxicity. In contrast, light-sheet fluorescence microscopy (LSFM) largely avoids exciting out-of-focus fluorescence, thereby enabling volumetric imaging with low photobleaching and intrinsic optical sectioning. Combining SIM with LSFM would enable gentle three-dimensional (3D) imaging at doubled resolution. However, multiple orientations of the illumination pattern, which are needed for isotropic resolution doubling in SIM, are challenging to implement in a light-sheet format. Here we show that multidirectional structured illumination can be implemented in oblique plane microscopy, an LSFM technique that uses a single objective for excitation and detection, in a straightforward manner. We demonstrate isotropic lateral resolution below 150 nm, combined with lower phototoxicity compared to traditional SIM systems and volumetric acquisition speed exceeding 1 Hz.