This paper suggests bivariate semiparametric index models as a tool for modelling the interplay of socioeconomic and health characteristics in determining health-care utilisation. These models allow for a fully nonparametric relationship between socioeconomic status, health-care need and care utilisation. The only parametric restriction imposed is that multiple socioeconomic and health indicators can be aggregated into two distinct indices that measure the broader concepts of socioeconomic status and health-care need, respectively. We demonstrate the usefulness of this class of models based on an illustrative empirical example. The estimations highlight complex interactions of socioeconomic status and health-care need in determining care use, which may be difficult to grasp via standard parametric modelling approaches.