The adsorption of a single and negatively charged polyion with varying flexibility onto a surface carrying both negative and positive charges representing a charged membrane surface has been investigated by using a simple model employing Monte Carlo simulations. The polyion was represented by a sequence of negatively charged hard spheres connected with harmonic bonds. The charged surface groups were also represented by charged hard spheres, and they were positioned on a hard surface slightly protruding into the solution. The surface charges were either frozen in a liquidlike structure or laterally mobile. With a large excess of positive surface charges, the classical picture of a strongly adsorbed polyion with an extended and flat configuration emerged. However, adsorption also appeared at a net neutral surface or at a weakly negatively charged surface, and at these conditions the adsorption was stronger with a flexible polyion as compared to a semiflexible one, two features not appearing in simpler models containing homogeneously charged surfaces. The presence of charged surface patches (frozen surface charges) and the ability of polarization of the surface charges (mobile surface charges) are the main reasons for the enhanced adsorption. The stronger adsorption with the flexible chain is caused by its greater ability to spatially correlate with the surface charges.