Non-scanning, single-shot, 3D integral microscopy with optical sectioning is presented. The method is based on the combination of Fourier-mode integral microscopy with a 3D deconvolution technique. Specifically, the refocused volume provided by a regular back-projection algorithm is 3D deconvolved with a synthetic 3D impulse response function that takes into account the number and positions of the elemental images. The use of this hybrid technique provides a stack of true-color depth-refocused images with significant gain of optical sectioning. The stack can be used, among other applications, to inspect inside the thick microscope specimen, to calculate collections of perspective views with fine angular resolution and extended full parallax, and also to display 3D images in an integral monitor. The method here presented is validated with both simulation and experimental data.