A weakness of standard 3D microscopies--both confocal and widefield+deconvolution-- is that their resolution is substantially worse in the axial direction than in the lateral plane. We describe two new widefield techniques with substantially improved axial resolution that actually exceeds the lateral resolution. As is well known, the resolution is related to the angle over which the objective lens collects light. In our first technique, light is collected over an enlarged set of angles by using two objective lenses on opposite sides of the sample. The two image beams are combined coherently on the same CCD camera. Interference between the beams yields new, previously inaccessible sample information. The second technique applies a similar concept to the illumination light in fluorescence microscopy. Light from an extended, spatially incoherent light source--such as a standard arc lamp--is split and directed through the two opposing objective lenses so as to create a narrow interference fringe at the focal plane in the sample. This spatial structure in the excitation light yields access to new sample information. The two techniques can easily be used together; the combined technique promises an axial resolution improvement of a factor of seven over standard widefield microscopy.