We propose an optimal stochastic scheduling strategy for a multi-vector energy complex (MEC), considering a full-blown model of the power-to-biomethane (PtM) process. Unlike conventional optimization that uses a simple efficiency coefficient to coarsely model energy conversion between electricity and biomethane, a detailed PtM model is introduced to emphasize the reactor kinetics and chemical equilibria of methanation. This model crystallizes the interactions between the PtM process and MEC flexibility, allowing to adjust the operating condition of the methanation reactor for optimal MEC operation in stochastic scenarios. Temperature optimization and flowsheet design of the PtM process increase the average selectivity of methane (i.e., ratio between net biomethane production and hydrogen consumption) up to 83.7% in the proposed synthesis flowsheet. Simulation results can provide information and predictions to operators about the optimal operating conditions of a PtM unit while improving the MEC flexibility.