This paper presents a new approach to assess and improve the environmental and economic performance of integrated electricity and heat district energy systems in light of (i) optimal operation of available multi-energy components (e.g., cogeneration and heat pumps) and (ii) energy exchanges within the district through internal electricity and heat networks. The latter is particularly attractive as, instead of constraining energy flows within each building, it enables the production and consumption of energy in the most attractive locations (e.g., in buildings that can accommodate photovoltaic panels). The proposed methodology is formulated as a mixed integer linear programming problem, and demonstrated with a real UK district comprising internal electricity and heat networks and several buildings. The results highlight the attractiveness of optimising multiple energy vectors, particularly in light of energy exchanges between buildings, in economic and environmental terms.