Lately, Integral-Imaging systems have shown very promising capabilities of capturing the 3D structure of micro- scopic and macroscopic scenes. The aim of this work is to provide an optimal design for 3D-integral microscopy with extended depth of field and enhanced lateral resolution. By placing an array of microlenses at the aperture stop of the objective, this setup provides a set of orthographic views of the 3D sample. Adopting well known integral imaging reconstruction algorithms it can be shown that the depth of field as well as spatial resolution are improved with respect to conventional integral microscopy imaging. Our claims are supported on theoretical basis and experimental images of a resolution test target, and biological samples.