This article investigates the double event-triggered consensus of positive multiagent systems with disturbance based on proportional integral observers (PIOs). First, PIOs concerning state and disturbance are designed, respectively. Then, a double event-triggered mechanism is presented: One is used to reduce the communication frequency between agents and their observers and the other one is used to reduce the communication frequency between agents and the corresponding control protocols. Moreover, a novel consensus framework is constructed for the systems by introducing a set of new variables, where an additional constant term is added to error dynamics. By constructing a copositive Lyapunov function, the positivity and stability of the systems are reached under the designed proportional integral state and disturbance observers. The gain matrices of the observers and control protocols are formulated via a matrix decomposition technique and computed in terms of linear programming. Finally, one example is presented to verify the effectiveness of the consensus algorithm.