Load transportation with quadruped robots is strongly affected by the dynamics of the physical interface between the robot and the load. Passive spring-based arms provide a lightweight and mechanically compliant alternative to active manipulators, but their dynamics can store and release energy during locomotion, producing oscillatory interaction forces that reduce robot stability. This paper develops a passive-arm-aware ZMP model for a quadruped carrying a payload through a passive arm. The reduced analytical model relates passive-interface stiffness, damping, and payload mass to the ZMP response under both external payload forcing and locomotion-induced base excitation, showing that lightly damped passive modes can overlap with gait harmonics. We then propose an arm-aware MPC (ARMPC), a passive-arm Model Predictive Control approach based on extended Single Rigid Body Dynamics that combines reduced floating-base dynamics with passive-arm joint states, internal torsional springs and dampers, and base-arm inertial coupling. Simulation ablations show that ARMPC consistently reduces ZMP-margin violations and prevents failures across all tested conditions, while Nominal MPC, which neither models nor compensates the passive arm, and Baseline MPC, which compensates it through an estimated wrench, exhibit higher violation percentages and failures under disturbances. Hardware pull-release experiments with a 2 kg payload show that the proposed ARMPC completes all longitudinal and diagonal disturbance trials without failure, whereas Baseline MPC fails in 7/15 and 8/15 trials, respectively. The same model also enables passive-arm end-effector tracking while maintaining a positive ZMP margin.

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