The aberration-corrected scanning transmission electron microscope (STEM) has emerged as a key tool for atomic resolution characterization of materials, allowing the use of imaging modes such as Z-contrast and spectroscopic mapping. The STEM has not been regarded as optimal for the phase-contrast imaging necessary for efficient imaging of light materials. Here, recent developments in fast electron detectors and data processing capability is shown to enable electron ptychography, to extend the capability of the STEM by allowing quantitative phase images to be formed simultaneously with incoherent signals. We demonstrate this capability as a practical tool for imaging complex structures containing light and heavy elements, and use it to solve the structure of a beam-sensitive carbon nanostructure. The contrast of the phase image contrast is maximized through the post-acquisition correction of lens aberrations. The compensation of defocus aberrations is also used for the measurement of three-dimensional sample information through post-acquisition optical sectioning.