In photoionization microscopy experiments, an atom is placed in static external fields, it is ionized by a laser, and an electron falls onto a position-sensitive detector. The current of electrons arriving at various points on the detector depends upon the initial state of the atom, the excited states to which the electron is resonantly or nonresonantly excited, and the various paths leading from the atom to the final point on the detector. We report here quantum-mechanical computations of photoionization microscopy in parallel electric and magnetic fields. We focus especially on the patterns resulting from resonant excited states. We show that the magnetic field substantially modifies some of these resonant states, confining them in the radial direction, and that it has a strong effect on the interference pattern at the detector.