Resilience of Critical Infrastructure (CI) has been a research focus for several years now, with efforts being made to develop methods for the analysis and assessment of CI resilience. However, these efforts are often carried out without consideration of enriching societal risk or resilience assessments with knowledge of the resilience of CI. Bearing in mind that the definition of CI according to the EU reflects the fact that it exists to deliver vital societal functions, the consideration of its resilience in isolation of the community it serves is only addressing part of the problem. The Horizon 2020 project IMPROVER has already developed methodologies for assessing and managing CI resilience. This paper proposes an evolution of the management framework for CI resilience which enriches societal resilience assessment with knowledge of the CI resilience. The framework and societal resilience analysis methodology are both described along with an application of the analysis method.