It is widely recognized that poverty is a multidimensional phenomenon involving not only income, but also other aspects such as education or health. In this multidimensional setting, analyzing the dependence between dimensions becomes an important issue, since a high degree of dependence could exacerbate poverty. In this paper, we propose measuring the multivariate dependence between the dimensions of poverty in Europe using copula‐based methods. This approach focuses on the positions of individuals across dimensions, allowing for other types of dependence beyond linear correlation. In particular, we analyze how orthant dependence between the dimensions of the AROPE rate has evolved in the EU‐28 countries between 2008 and 2014 by applying non‐parametric estimates of multivariate copula‐based generalisations of Spearman’s rank correlation coefficient. We find a general increase in the dependence between dimensions, regardless of the coefficient used. Moreover, countries with higher AROPE rates also tend to experiment more dependence between its dimensions.