A multiplex social network captures multiple types of social relations among the same set of people, with each layer representing a distinct type of relationship. Understanding the structure of such systems allows us to identify how social exchanges may be driven by a person's own attributes and actions (independence), the status or resources of others (dependence), and mutual influence between entities (interdependence). Characterizing structure in multiplex networks is challenging, as the distinct layers can reflect different yet complementary roles, with interdependence emerging across multiple scales. Here, we introduce the Multiplex Latent Trade-off Model (MLT), a framework for extracting roles in multiplex social networks that accounts for independence, dependence, and interdependence. MLT defines roles as trade-offs, requiring each node to distribute its source and target roles across layers while simultaneously distributing community memberships within hierarchical, multi-scale structures. Applying the MLT approach to 176 real-world multiplex networks, composed of social, health, and economic layers, from villages in western Honduras, we see core social exchange principles emerging, while also revealing local, layer-specific, and multi-scale communities. Link prediction analyses reveal that modeling interdependence yields the greatest performance gains in the social layer, with subtler effects in health and economic layers. This suggests that social ties are structurally embedded, whereas health and economic ties are primarily shaped by individual status and behavioral engagement. Our findings offer new insights into the structure of human social systems.