There are many existing buildings for which seismic rehabilitation interventions are required, especially in earthquake-prone areas like Italy. At the same time, the huge energy cost increase in Europe highlights the need for sustainable techniques that are able to increase the energy efficiency of buildings. These issues are even more significant for weak social groups living in social housing buildings, often in poor and vulnerable conditions. In order to address the solution regarding building renovations from the social, structural, and energy efficiency perspectives, in the framework of the Horizon Europe REHOUSE (Renovation packagEs for HOlistic improvement of EU’s bUildingS Efficiency, maximizing RES generation and cost-effectiveness) Project, this paper proposes an integrated methodology of building assessment that was tested on a social housing building in Margherita di Savoia, a small town of Apulia Region, Italy. In addition to the structural and energy aspects, the social one is particularly important since the building is located in the “Capitanata Area”, considered to be one of the most socially vulnerable areas in Italy. For this reason, an assessment methodology must consider reducing the overall impact of the assessment activities while explaining to tenants the purpose of the assessment and future renovation actions, maintaining the accuracy of the assessment results. Therefore, this study outlines an assessment methodology, demonstrated through its application to the case study building, that integrates the structural, energy, and social aspects, showing that the tenants’ involvement is also crucial for the technical evaluations. The final result is a low-impact approach for the building knowledge gathering needed to start a deep renovation intervention in social housing.