The way in which natural and physical capital are accumulated, distributed and harnessed underpins the functioning and sustainability of the productive system of each society as well as its social stratification. Significant changes in the interactions between natural and physical capital accumulation give rise to processes of structural change (SC) which affect not only sectoral composition of the productive system, but also social equity and environmental quality. We propose a taxonomy of different SCs on the basis of distributive, environmental and economic outcomes and we study a two-sector model with environmental externalities to identify under which conditions each SC can occur. Our model shows how the type of SC is shaped by the link between agents' heterogeneity in terms of productive asset endowment and their vulnerability to environmental degradation. In particular, we find that a SC associated with reduction in poverty and in environmental pressures can occur only if productivity of the physical capital-intensive sector increases but its rate of environmental impact remains relatively lower than that of the natural-capital intensive sector.