Due to the use of ramjet engines, the air-breathing missile adopts the BTT control method. Aiming at the channel coupling, strong nonlinearity, and fast time-varying problems of BTT missiles intercepting highly maneuvering targets, an integrated guidance and control method for BTT missiles intercepting highly maneuvering targets considering channel coupling is proposed. Firstly, a three-dimensional integrated guidance and control model for BTT missiles intercepting maneuvering targets considering coupling factors between control channels and engine boost is established. Next, the uncertainties in the model are treated as disturbances, and an extended state observer is designed to compensate for the disturbances. Then the stability of the system is proved. Finally, numerical simulation verifies that the method proposed in this paper is suitable for the fast time-varying control requirements of BTT missiles with strong coupling when intercepting large maneuvering targets.