Lipopolysaccharide (LPS) is a key surface component of Gram-negative bacteria, populating the outer layer of their outer membrane. A number of experimental studies highlight its protective role against harmful molecules such as antibiotics and antimicrobial peptides (AMPs). In this work, we present a theoretical model for describing the interaction between LPS and cationic antimicrobial peptides, which combines the following two key features. The polysaccharide part is viewed as forming a polymer brush, exerting an osmotic pressure on inclusions such as antimicrobial peptides. The charged groups on LPS (those in lipid A and the two Kdo groups in the inner core) form electrostatic binding sites for cationic AMPs or cations. Using the resulting model, we offer a quantitative picture of how the brush component enhances the protective role of LPS against magainin-like peptides, in the presence of divalent cations such as Mg2+. The LPS brush tends to diminish the interfacial binding of the peptides, at the lipid headgroup region, by about 30%. In the presence of 5 mM of Mg2+, the interfacial binding does not reach a threshold value for wild-type LPS, beyond which the LPS layer is ruptured, even though it does for LPS Re (the simplest form of LPS, lacking the brush part), as long as [AMP] ≤ 20 μM, where [AMP] is the concentration of AMPs. At a low concentration of Mg2+ (≈1 mM), however, a smaller [AMP] value (≳2 μM) is needed to reach the threshold coverage for wild-type LPS. Our results also suggest that the interfacial binding of peptides is insensitive to their possible weak interaction with the surrounding brush chains.