The adsorption of colloids of varying sizes and charges onto a surface that carries both negative and positive charges, representing a membrane, has been investigated using a simple model employing Monte Carlo simulations. The membrane is made of positive and negative charges (headgroups) that are allowed to move along the membrane, simulating the translational diffusion of the lipids, and are also allowed to protrude into the solution, giving rise to a fluid and soft membrane. When an uncharged colloid is placed in the vicinity of the membrane, a short-range repulsion between the colloid and the membrane is observed and the membrane will deflect to avoid coming into contact with the colloid. When the colloid is charged, the membrane response is twofold: the headgroups of the membrane move toward the colloid, as if to partly embrace it, and the positive headgroups of the membrane approach the oppositely charged colloid, inducing the demixing of the membrane lipids (polarization). The presence of protrusions enhances the polarization of the membrane. Potential of mean force calculations show that protrusions give rise to a more long-range attractive colloid-membrane potential which has a smaller magnitude at short separations.