In this work, we consider adjacent channel interference (ACI) cancellation in the dual satellite communication system which supports simultaneous uplink and downlink communications between an airplane and two satellites over adjacent frequency bands. The transmitter of the uplink communication toward one satellite creates strong ACI to the receiver on the downlink from the second satellite to the airplane. Most ACI cancellation techniques in the literature consider the scenario where both interfering and interfered signals have identical bandwidth (and same symbol rate) where our design is motivated by the uplink/downlink communications between an airplane and Iridium/Inmarsat satellites which happen over frequency bands of different sizes (hence, different symbol rates) for which the conventional ACI cancellation techniques are not applicable. Toward this end, we present the signal and system models for simultaneous communications on adjacent bands with different bandwidths and propose a constant-norm Least Square (CN-LS) based interference cancellation strategy. Our design also addresses the nonlinearity of the High Power Amplifier (HPA) where the first and third order interference terms are identified and canceled out by using the Volterra filter. We demonstrate through numerical studies that our design is robust against the frequency spacing and significantly outperforms the conventional detection scheme without ACI cancellation.