Increasing percentages of distributed generators in active distribution networks (ADNs) have increased the concern on excess generations in the medium and low voltage levels. High capacities of excess power are mainly from intermittent wind, solar power, and the restricted power generations of combined heat and power (CHP) plants, which are determined by the heat demand. Turning excess power to hydrogen has been recognized as a promising method to meet potential hydrogen demand from the traffic sectors. Nevertheless, it suffers from a low power-to-hydrogen efficiency, which is usually below 70% for commercialized electrolysis. By introducing in the heat recovery at the system level, we propose an integrated solution to supply heat to district heating networks (DHNs) while producing hydrogen, i.e., a power-to-hydrogen-and-heat scheme (P2HH). The extra benefit of P2HH resulting from heat supply is the reduction in the output of CHP, which reduces the excess energy in ADNs. This paper establishes a detailed 'T-H-H' model to couple the power-to-heat and power-to-hydrogen processes. Then, a simplified P2HH dispatch model is proposed for the electricity-heat-hydrogen dispatch coordinated with ADN and DHN. Finally, the overall benefits of P2HH via improving the system economy and security are demonstrated with a modified IEEE 33-node system.