This paper proposes a two-parameter family of socio-economic health inequality indices. First, these indices allow a Boolean risk factor to be linked to other health dimensions. Second, multidimensional health distributions can be compared thanks to a stochastic dominance rule, which includes the attitude of the social planner with respect to the risk factor (risk neutrality, risk aversion and extreme risk aversion). Third, each order of stochastic dominance is also associated with the intensity of possible health transfers occurring between individuals, that is, the degree of inequality aversion of the social planner. This approach is a multidimensional extension of Yitzhaki’s Gini indices accounting simultaneously for risk and redistribution.