The increasing frequency of high-impact, low-probability (HILP) events poses a serious threat to modern distribution systems, motivating a shift from robustness toward resilience-oriented operation. In urban lifeline systems, the power distribution system (PDS) and the water distribution system (WDS) are tightly interdependent, since water pumping is energy-intensive and any power outage propagates directly into water shortages. Restoration strategies that treat the two networks separately therefore overlook important coordination opportunities and may allocate scarce resources inefficiently. Most existing models address either the electrical reconfiguration of the power network or the hydraulic operation of the water network and rarely incorporate comprehensive demand response (DR). This paper proposes a fully linearized mixed-integer linear programming (MILP) framework for the resilience-oriented restoration of coupled PDS and WDS. The operational constraints of both infrastructures, including network reconfiguration; distributed energy resource (DER) dispatch (including diesel generators (DGs), photovoltaic (PV) units, and electrical energy storages (EESs)); hydraulic head losses; variable-speed pump dynamics; and tank storage, are embedded within a single model and coordinated through nexus constraints together with three DR programs. The nonlinearities of the Hazen–Williams equation and the pump characteristics are systematically linearized to preserve tractability. The framework is evaluated on a coupled IEEE 33-bus power system and a 15-node water network under a severe fault scenario. The results reveal that hydraulic flexibility is the dominant restoration mechanism, while DR provides a complementary improvement, and their coordinated use delivers the most effective recovery of both infrastructures.