Context :

Aims : We aim at analysing systematically the distribution and physical properties of neutral and mildly ionised gas in the Milky Way halo , based on a large absorption-selected data set .

Methods : Multi-wavelength studies were performed combining optical absorption line data of Ca ii and Na i with follow-up H i 21-cm emission line observations along 408 sight lines towards low- and high-redshift QSOs .
We made use of archival optical spectra obtained with UVES/VLT .
H i data were extracted from the Effelsberg-Bonn H i survey and the Galactic All-Sky survey .
For selected sight lines we obtained deeper follow-up observations using the Effelsberg 100-m telescope .

Results : Ca ii ( Na i ) halo absorbers at intermediate and high radial velocities are present in 40 - 55 % ( 20 - 35 % ) of the sightlines , depending on the column density threshold chosen .
Many halo absorbers show multi-component absorption lines , indicating the presence of sub-structure .
In 65 % of the cases , absorption is associated with H i 21-cm emission .
The Ca ii ( Na i ) column density distribution function follows a power-law with a slope of \beta \approx - 2.2 ( -1.4 ) .

Conclusions : Our absorption-selected survey confirms our previous results that the Milky Way halo is filled with a large number of neutral gas structures whose high column density tail represents the population of common H i high- and intermediate-velocity clouds seen in 21-cm observations .
We find that Ca ii /Na i column density ratios in the halo absorbers are typically smaller than those in the Milky Way disc , in the gas in the Magellanic Clouds , and in damped Lyman \alpha systems .
The small ratios ( prominent in particular in high-velocity components ) indicate a lower level of Ca depletion onto dust grains in Milky Way halo absorbers compared to gas in discs and inner regions of galaxies .