The optical microscope is customarily an instrument of substantial size and expense but limited performance. Here we report an integrated microscope that achieves optical performance beyond a commercial microscope with a 5×, NA 0.1 objective but only at 0.15 cm3and 0.5 g, whose size is five orders of magnitude smaller than that of a conventional microscope. To achieve this, a progressive optimization pipeline is proposed which systematically optimizes both aspherical lenses and diffractive optical elements with over 30 times memory reduction compared to the end-to-end optimization. By designing a simulation-supervision deep neural network for spatially varying deconvolution during optical design, we accomplish over 10 times improvement in the depth-of-field compared to traditional microscopes with great generalization in a wide variety of samples. To show the unique advantages, the integrated microscope is equipped in a cell phone without any accessories for the application of portable diagnostics. We believe our method provides a new framework for the design of miniaturized high-performance imaging systems by integrating aspherical optics, computational optics, and deep learning.