We have studied ultrathin Cu ยฎlms grown on three related ferromagnetic (FM) layers to clarify the role of the substrate in determining the two-dimensional dispersion of metallic quantum well (MQW) states in the overlayer. The dispersions with parallel momentum of Cu MQW states above the Fermi level E F were measured in the Cu/fccFe/Cu(1 0 0) and Cu/fccCo/ Cu(1 0 0) systems using inverse photoemission, and below E F in the Cu/fccNi/Cu(1 0 0) system using angle resolved photoemission spectroscopy. This study focussed on the CX direction of the two-dimensional Brillouin zone. For states away from the projected band gaps of the FM layer, the identity of the FM layer (i.e., Fe or Co) has little inยฏuence on Cu MQW states and their dispersions closely resemble those of a free standing Cu ยฎlm. In contrast, all three systems exhibit nondispersing MQW states when the Cu bands overlap the minority spin projected band gaps of the FM metal. A phase accumulation approach gives a very simple explanation of this behavior, showing that the ยฏat dispersion occurs because the phase shift upon reยฏection from the FM layer has a strong energy dependence in the projected gap.