The increasing frequency of environmental events driven by global warming poses a significant threat to smart network operations, highlighting the need for advanced self-healing techniques to enhance grid stability and accelerate recovery during emergencies. This study proposes a two-stage distributed optimization mechanism for self-healing in coupled electricity and gas networks. The mechanism leverages the capabilities of smart prosumers, such as industrial parks, charging stations, and power-to-hydrogen (P2H) units, to minimize load shedding and bolster resilience under emergency conditions. In the first stage, the distribution system operator optimally reconfigures electricity and gas networks, plans distribution feeder operations, and deploys fuel cell-equipped trucks to allocate the required power and gas capacities to smart prosumers via signal pulses. The second stage focuses on modeling the smart prosumers, enabling them to offer their available capacities to the network operator in response to these signals. To ensure secure convergence with minimal information exchange between the two stages, an augmented Alternating Direction Method of Multipliers (ADMM) algorithm is utilized. The proposed mechanism was validated on two different test systems, solved using the GUROBI solver within GAMS. Simulation results demonstrate that the mechanism effectively harnesses maximum capacities from smart prosumers, reducing load shedding by 64.08 % and improving the resilience index by 80.34 %. Furthermore, the augmented ADMM enhanced computational efficiency, achieving a 45.3 % faster solution compared to the standard version while ensuring global optimality.