Absorbing layers of a low-emissivity (low-E) coating are designed to cause the coating to have a reduced film side reflectance which is advantageous for aesthetic purposes. In certain embodiments, the absorbing layers are metallic or substantially metallic (e.g., NiCr or NiCrNx) and are positioned in order to reduce or prevent oxidation of the absorbing layers during optional heat treatment (e.g., thermal tempering, heat bending, and/or heat strengthening). Coated articles according to certain example embodiments of this invention may be used in the context of insulating glass (IG) window units, other types of windows, etc.