In recent years, the concepts of footprint family and planetary boundaries have both received considerable popularity in the field of sustainability science. By reviewing the conceptual roots of these two concepts, we argue that they are complements to each other and thus should be used collectively in assessing the environmental sustainability of the planet, nations, regions, etc. Building on the complementary nature of the footprint and boundary indicators, this paper proposes, for the first time, a framework for defining and assessing environmental sustainability from a novel point of view, in which the footprints and boundaries are measured and compared in a coherent manner. The footprint family is defined as a measure of the regenerative and absorptive capacity of the Earth's ecosystems to satisfy mankind's demand for natural resources and waste emissions. The planetary boundaries are defined as a measure of the Earth's maximum regenerative and absorptive capacity that allows to define a safe operating space for humanity. As such, environmental sustainability can be simply defined as a safe state in which man's environmental footprints are kept within the related planetary boundaries; otherwise it refers to environmental unsustainability. The environmental sustainability concept is featured by completeness, selectivity, interactivity, uncertainty, scale-dependence, and the negotiability of environmental deficit. The implications of the footprint-boundary integrated framework are illustrated by reference to the assessment and ranking of 30 major nations' environmental sustainability with regard to carbon emissions (climate change), water use and land use. The results show that, in the case of carbon emissions, 22 nations are found to be unsustainable, of which the United States of America has the highest carbon deficit per capita of 26.1 t·a~(-1) (in CO_2 equivalent). In the case of water use, Spain, which has a water deficit per capita of 1 497.8 m~3·a~(-1), ranks the highest among the 17 nations that are found to be unsustainable. In the case of land use, the Dutch land deficit per capita (2.3 hm~2·a~(-1)) is significantly larger than that of other 14 nations which are classified as unsustainable. Our findings suggest that the sustainability of carbon emissions is in close relation to the nation's level of social and economic development. The contribution of developed countries to global climate change, therefore, appears to be much higher than that of developing countries. The sustainability of water and land use is often driven by the average amount of water and land resource within the border of the nation that can be appropriated by an individual citizen. This paper provides a reference for quantifying and ranking the national performance on environmental sustainability. The framework established can also be applied to other environmental issues or at sub-national scales.