A new type of wide-field fluorescence microscopy is described, which produces 100-nm-scale spatial resolution in all three dimensions, by using structured illumination in a microscope that has two opposing objective lenses. Illumination light is split by a grating and a beam splitter into six mutually coherent beams, three of which enter the specimen through each objective lens. The resulting illumination intensity pattern contains high spatial frequency components both axially and laterally. In addition, the emission is collected by both objective lenses coherently, and combined interferometrically on a single camera, resulting in a detection transfer function with axially extended support. These two effects combine to produce near-isotropic resolution. Experimental images of test samples and biological specimens confirm the theoretical predictions.