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 photo-bleaching and intrinsic optical sectioning. Combining SIM with LSFM would enable gentle 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, a LSFM technique that uses a single objective for excitation and detection, in a straightforward manner. We demonstrate isotropic lateral resolution below 150nm, combined with lower photo-toxicity compared to traditional SIM systems and volumetric acquisition speed exceeding 1Hz.