Conventional confocal microscopes are based on the dual scanning of a specimen by the images of a point source and of a point detector. Hence, their imaging mode is serial, i.e., the confocal image is obtained from the sequence of single-point or multiple-point partial images. Parallel-mode confocal imaging is possible on the basis of broad- source image-plane holography. We adapted this classical holography technique for real-time reflected-light microscopy. The imaging speed of the parallel-mode confocal microscope is not limited by any part of the optical system, but only by the image detection and storage systems. Both the image phase and the image amplitude are reconstructed from the interference signal. We verify both theoretically and experimentally that the main imaging parameters of the microscope are comparable with those of a conventional confocal microscope. The only exception is the imaging speed, which can be much higher.