We present the control in physical interaction with the environment of a Cable-suspended Aerial Multi-Robot Manipulator (CS-AMRM) called the Fly-Crane, composed of three aerial vehicles towed to a platform by means of six cables. The control strategy enables the system to accurately and safely perform tasks involving expected or unexpected interactions between the platform and the environment, in the absence of dedicated force/torque sensors. A previously developed Inverse Kinematic Controller (IKC) is enhanced with an admittance framework, and contacts are estimated through a generalized momentumbased observer. To assess the validity of our approach, and to provide practical insights into the method, we perform extensive experimental tests, comprehending the admittance property shaping to modulate stiffness, damping, and virtual mass, as well as experiments in a more realistic scenario involving contacts between the Fly-Crane and the environment.