Stormwater runoff from roadways often contains a variety of contaminants such as heavy metals, which can adversely impact receiving waters. The filter media in stormwater filtration/infiltration systems play a significant role in the simultaneous removal of multiple pollutants. In this study, the capacity of five filter media—natural quartz sand (QS), sandy soil (SS) and three mineral-based technical filter media (TF-I, TF-II and TF-III)—to adsorb heavy metals (Cu, Pb and Zn) frequently detected in stormwater, as well as remobilization due to de-icing salt (NaCl), were evaluated in column experiments. The column breakthrough data were used to predict lifespan of the filter media. Column experiment operated under high hydraulic load showed that all technical filters and sandy soil achieved >97%, 94% and >80% of Pb, Cu and Zn load removals, respectively, while natural quartz sand (QS) showed very poor performance. Furthermore, treatment of synthetic stormwater by the soil and technical filter media met the requirements of the Austrian regulation regarding maximum effluent concentrations and minimum removal efficiencies for groundwater protection. The results showed that application of NaCl had only a minor impact on the remobilization of heavy metals from the soil and technical filter media, while the largest release of metals was observed from the QS column. Breakthrough analysis indicated that load removal efficiencies at column exhaustion (SS, TF-I, TF-II and TF-III) were >95% for Cu and Pb and 80–97% for Zn. Based on the adsorption capacities, filtration systems could be sized to 0.4 to 1% (TF-I, TF-II and TF-III) and 3.5% (SS) of their impervious catchment area and predicated lifespan of each filter media was at least 35, 36, 41 and 29 years for SS, TF-I, TF-II and TF-III, respectively. The findings of this study demonstrate that soil—based and technical filter media are effective in removing heavy metals and can be utilized in full-stormwater filtration systems.