We present a survey of satellites around a homogeneous set of late-type spirals with luminosity similar to that of the Milky Way. On average, we find fewer than 1.5 satellites per primary, but we argue that we can treat the survey as an ensemble and so derive the properties of the halo of a 'typical' isolated spiral. The projected density profile of the ensemble falls off approximately as 1/r. Within 50 kpc the azimuthal distribution of satellites shows some evidence for the 'Holmberg effect', an excess near the minor axis of the primary; however, at larger projected distances, the distribution appears isotropic. There is a weak but significant correlation between the size of a satellite and its distance from its primary, as expected if satellites are tidally truncated. Neither Hubble type nor spectral characteristics correlate with apparent separation. The ensemble of satellites appears to be rotating at about 30 km/s in the same direction as the galactic disk. Satellites on prograde orbits tend to be brighter than those on retrograde orbits. The typical velocity difference between a satellite and its primary shows no clear dependence either on apparent separation, or on the rotation speed of the primary. Thus our survey demonstrates that isolated spiral galaxies have massive halos that extend to many optical radii.