We have observed the Virgo cluster spiral NGC 4569 in X-rays with ROSAT (0.1-2.4 keV) and in the optical. From the PSPC image one can distinguish different components, like the dominant source in the nuclear region, the galactic disk, and a diffuse soft component extended to the west. This latter one coincides with a giant Hα structure. In both spectral ranges the structure reaches up to 9 kpc out of the disk. This coincidence, the soft X-ray energy distribution, and the existence of a central starburst in NGC 4569 let us conclude that the X-ray gas traces a large scale outflow from accumulating supernova explosions and stellar winds in the galactic center. The resulting physical properties of this X-ray halo are comparable to those derived from X-ray halos in edge-on galaxies, like e.g. NGC 253. We also discuss the influence of the intracluster medium on the observed X-ray and Hα morphology. The spectral 0.1-2.4 keV distribution of the central source and the X-ray-to-Hα luminosity ratio favour a supermassive star cluster at the very compact core rather than an accretion-powered active nucleus in agreement with the absence of a hard compact X-ray source in the ASCA band. The nearby Magellanic dwarf galaxy IC 3583 at a projected distance of only 30 kpc reveals an unresolved X-ray point source, several blue knots in the optical, and a narrow Hα spur, pointing toward NGC 4569, detected also in the B band image. This is an indication for ongoing star formation also in IC 3583. Some interaction with NGC 4569 will be discussed although the relative radial velocity between both objects of about 1300 km s-1 makes it rather unlikely.