In the production of metal-polymer multilayer composite parts, e.g., for automotive applications, the possibilities of thermal joining are limited due to the instability of the polymer core at elevated temperatures. Accordingly, such materials require a special approach to their welding. The three-layered metal-polymer-metal samples were made of DPK 30/50+ZE dual-phase steel as cover sheets that were electrolytic galvanized, and a polypropylene-polyethylene foil as core material, with thicknesses of 0.48/0.3/0.48 mm. The samples were welded on both sides using a 1.06 µm Nd:YAG ROFIN StarWeld Manual Performance laser. Significant improvements of the welding conditions are achieved by machining the edges of materials to be welded. The parameters of laser welding were chosen in such a way that the polymer structure remained almost unchanged. The weld thickness was about 40% of the thickness of each steel layer. It was established that within the selected laser processing parameters the melting occurred uniformly, while the polymer layer practically did not change its structure. Therefore, it can be stated that two-sided joint welding of metal-polymer-metal composite sandwich panels, without significant degradation of the polymer core layer, is feasible.