Context. Since 1973, it has been known that some Hi high velocity clouds (HVCs) have a core-envelope structure. Recent observations of compact HVCs confirm this, but more general investigations have been missing so far. Aims. We study the properties of all major HVC complexes from a sample compiled in 1991 by Wakker & van Woerden (WvW). Methods. We use the Leiden/Argentine/Bonn all sky 21-cm line survey and decompose the profiles into Gaussian components. Results. We find the WvW line widths and column densities to be underestimated by similar to 40%. In 1991, these line widths could not be measured directly, but had to be estimated with the help of higher resolution data. We find a well-defined multi-component structure for most of the HVC complexes. The cold HVC phase has lines with typical velocity dispersions of sigma = 3 km s(-1) and exists only within more extended broad line regions, typically with sigma = 12 km s(-1). The motions of the cores relative to the envelopes are characterized by Mach numbers M = (upsilon(core)-upsilon(envelope))/sigma(envelope) similar to 1.5. The center velocities of the cores within a HVC complex have typical dispersions of 20 km s(-1). The well-defined two-component structure of some prominent HVC complexes in the outskirts of the Milky Way is remakable: Complex H lies approximately in the Galactic plane, and the most plausible distance estimate of R similar to 33 kpc places it at the edge of the disk. The Magellanic Stream and the Leading Arm (complex EP) reach higher latitudes and are probably more distant, R similar to 50 kpc. There might be some indications for an interaction between HVCs and disk gas at intermediate velocities. This is possible for complex H, M, C, WB, WD, WE, WC, R, G, GCP, and OA, but not for complex A, MS, ACVHV, EN, WA, and P. Conclusions. The line widths, determined by us, imply that estimates of HVC masses, as far as those derived from the WvW database are concerned, need to be scaled up by a factor 1.4. Correspondingly, guesses for the external pressure of a confining coronal gas need to be revised upward by a factor of 2. The HVC multi-phase structure implies in general that currently the halo pressure is significantly underestimated. In consequence, the HVC multi-phase structure may indicate that most of the complexes are circumgalactic. HVCs have turbulent energy densities which are an order of magnitude larger than that of comparable clumps in the Galactic disk.
