This paper presents an original approach aimed at combining the emerging concepts of resilience and sustainability of infrastructure systems, bridges in particular. Resilience is a metric of the impact that the bridge has on the society when subjected to extreme events, such as earthquakes. On the other hand, sustainability analyses attempt to quantify the impact of the bridge on several issues of concern for the society (e.g. health, biodiversity, land use, etc.) under ordinary conditions. Nowadays, both resilience and sustainability should be considered when a new infrastructure system is designed. However, since they have always been treated separately, their combination presents challenges and requires trade-offs. In this paper it is proposed to merge resilience and sustainability in a general probabilistic framework rooted in risk theory.