The studies aimed to test the adsorption capacity of two silica-enriched porous materials, synthetic Na-X zeolite and Mn-containing carbon composite, towards Pb(II) and Zn(II) ions in single and mixed systems and in the presence of diclofenac (DCF) and (or) poly(acrylic acid) (PAA). The synthetic zeolite was characterized by a well-developed surface area of 728 m2/g and a pore diameter of 1.73 nm, while the carbon composite exhibited 268 m2/g and 7.37 nm, respectively. Na-X was found to be more efficient than the carbon composite (75–212 mg/g) in adsorbing heavy metal ions in both single and bimetallic systems (322–333 mg/g). In turn, the C/Mn/SiO2 composite was more effective in removing Pb(II) ions from the systems that simultaneously contained DCF or PAA (480 and 476 mg/g, respectively). The Na-X zeolite demonstrated the greatest stability in all the systems studied. The highest stability was observed in the DCF + Pb(II) mixture, in contrast to the carbon composites where the stability was much lower. To evaluate the possibility of regeneration of the solids, HCl proved to be the best desorbent for heavy metal ions (efficiency of 99%). In general, both adsorbents offer promising potential for solving environmental problems.