Imaging volumes as thick as whole cells at three-dimensional (3D) super-resolution is required to reveal unknown features of cellular organization. We report a light microscope that generates images with translationally invariant 30 x 30 x 75nm resolution over a depth of several micrometers. This method, named biplane (BP) FPALM, combines a double-plane detection scheme with fluorescence photoactivation localization microscopy (FPALM) enabling 3D sub-diffraction resolution without compromising speed or sensitivity.