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The scope of the current work is to present a fundamental unified framework to quantify and characterise the energy flexibility of electrical and thermal systems commonly found in residential buildings. A quantification framework applicable to multicomponent residential buildings is developed and the energy cost of various demand response actions in the context of locally produced energy is determined. A calibrated white-box model of a residential building using EnergyPlus is utilised towards this end and the associated results are aggregated to formulate daily mappings of energy flexibility. Simulations show that the flexibility potential of each component depends on multiple factors including, inter alia: weather, occupant preferences, energy conversion components, and building thermal characteristics.