Chemisorption of an isolated CO molecule at various adsorption sites above the epitaxial Pd overlayer on Ta(110), and on related systems, is studied by using a self-consistent tight-binding scheme. Basic assumptions of the model are discussed in detail. The sigma donation and especially the pi backdonation are generally a good deal reduced at the bimetallic surface as compared with the pure Pd(111) surface. Simultaneously, the bond between CO and the surface becomes weaker. However, for CO in the atop position the effect is considerably smaller than for sites with twofold or threefold coordination and the atop site can therefore become preferred. A simple bonding picture explaining the gross trends is suggested. Core-level shifts induced in surface atoms by the adsorption are briefly discussed.