Styrene-maleic acid (SMA) copolymers have recently gained attention for their ability to facilitate the detergent-free solubilization of membrane protein complexes and their native boundary lipids into polymer-encapsulated, nanosized lipid particles, referred to as SMALPs. However, the interfacial interactions between SMA and lipids, which dictate the mechanism, efficiency, and selectivity of lipid and membrane protein extraction, are barely understood. Our recent finding has shown that SMA 1440, a chemical derivative of the SMA family with a functionalized butoxyethanol group, was most active in galactolipid-rich membranes, as opposed to phospholipid membranes. In the present work, we have performed X-ray reflectometry (XRR) and neutron reflectometry (NR) on the lipid monolayers at the liquid-air interface followed by the SMA copolymer adsorption. XRR and Langmuir Pi-A isotherms captured the fluidifying effect of galactolipids, which allowed SMA copolymers to infiltrate easily into the lipid membranes. NR results revealed the detailed structural arrangement of SMA 1440 copolymers within the membranes and highlighted the partition of butoxyethanol group into the lipid tail region. This work allows us to propose a possible mechanism for the membrane solubilization by SMA.