The resolution of standard 3D optical microscopies--both confocal and widefield+deconvolution--is substantially worse in the axial direction than in the lateral plane. This weakness is caused by the fact that the objective lens in a conventional microscopy can only access light emitted within a limited angle of the optical axis. We are developing several new widefield techniques in which light is collected over a larger set of angles by using two separate, opposing objective lenses to observe and/or illuminate the sample from both sides simultaneously. This gives access to substantially more spatial information about the sample than can normally be reached. This information is in the form of relative phase correlations between the two image beams, and thus cannot be accessed by studying either beam alone, but can be detected through the interference of the two image beams if they are combined coherently on a single image detector. The added information allows computational 3D reconstruction to be made with drastically improved axial resolution compared to conventional widefield or confocal microscopies. Experimentally measured transfer functions from our prototype microscope show excellent qualitative agreement with theoretical expectations, and 3D reconstructions of test samples confirm the expected improvement in axial resolution.