We developed an X-ray microscope using partially coherent object illumination instead of previously used quasi-incoherent illumination. The design permitted the incorporation of a cryogenic tilt stage, enabling tomography of frozen-hydrated, intact adherent cells. We obtained three-dimensional reconstructions of mouse adenocarcinoma cells at ∼36-nm (Rayleigh) and ∼70-nm (Fourier ring correlation) resolution, which allowed us to visualize the double nuclear membrane, nuclear pores, nuclear membrane channels, mitochondrial cristae and lysosomal inclusions.