A disposable liquid absorbing cleaning pad for a mop includes a layer of sponge material, a layer of flexible open cell foam material made from melamine resin fixedly attached to the layer of sponge material and attachment structure secured to the layer of sponge material for removably attaching the cleaning pad to the mop. In using the cleaning pad, the layer of flexible open cell foam material made from melamine resin is the layer that contacts the surface to be cleaned. The cleaning pad may be provided with a suitable attachment structure for mounting the pad onto a butterfly mop, a squeeze mop or a roller mop.