Aims. Broad absorption-line quasars (BALQSOs) are key objects for studying the structure and emission/absorption properties of AGN. However, despite their fundamental importance, the properties of BALQSOs remain poorly understood. To investigate the X-ray nature of these sources, as well as the correlations between X-ray and rest-frame UV properties, we compile a large sample of BALQSOs observed by XMM-Newton. Methods. We collect information for 88 sources from the literature and existing catalogues, creating the largest BALQSO sample analysed optically and in X-ray to date. We performed a full X-ray spectral analysis (using unabsorbed and both neutral and ionized absorption models) on a sample of 39 sources with higher X-ray spectral quality, and an approximate hardness-ratio analysis on the remaining sources. Using available optical spectra, we calculate the BALnicity index and investigate the dependence of this optical parameter on different X-ray properties. Results. Using the neutral absorption model, we find that 36% of our BALQSOs have $N_{\rm H}^{n}$ < 5 × 1021 cm-2, lower than the expected X-ray absorption for these objects. However, when we used a physically-motivated model for the X-ray absorption in BALQSOs, i.e., ionized absorption, ~90% of the objects are absorbed. The observed difference in ionized properties of sources with the BALnicity index (BI) = 0 and BI > 0 might be explained by different physical conditions of the outflow and/or inclination effects. The absorption properties also suggest that LoBALs may be physically different objects from HiBALs. In addition, we report on a correlation between the ionized absorption column density and BAL parameters. There is evidence (at the 98% level) that the amount of X-ray absorption is correlated with the strength of high-ionization UV absorption. Not previously reported, this correlation can be naturally understood in virtually all BALQSO models, as being driven by the total amount of gas mass flowing towards the observer. We also find a hint of a correlation between the BI and the ionization level detected in X-rays.