Recent developments of molecular tools have revolutionized our knowledge of microbial biodiversity by allowing detailed exploration of its different facets and generating unprecedented amount of data. One key issue with such large datasets is the development of diversity measures that cope with different data outputs and allow comparison of biodiversity across different scales. Diversity has indeed three components: local (α), regional (γ) and the overall difference between local communities (β). Current measures of microbial diversity, derived from several approaches, provide complementary but different views. They only capture the β component of diversity, compare communities in a pairwise way, consider all species as equivalent or lack a mathematically explicit relationship among the α, β and γ components. We propose a unified quantitative framework based on the Rao quadratic entropy, to obtain an additive decomposition of diversity (γ = α + β), so the three components can be compared, and that integrate the relationship (phylogenetic or functional) among Microbial Diversity Units that compose a microbial community. We show how this framework is adapted to all types of molecular data, and we highlight crucial issues in microbial ecology that would benefit from this framework and propose ready-to-use R-functions to easily set up our approach.