We study by synchrotron small-angle x-ray scattering highly aligned lamellar phases of a zwitterionic surfactant, doped with monodisperse and spherical hydrophobic inorganic particles as a function of particle concentration. Analysis of the structure factor of the two-dimensional fluid formed by the particles in the plane of the bilayer gives access to their membrane-mediated interaction, which is repulsive, with a contact value of about 4kBT and a range of 14 angstroms. Systematic application of this technique should lead to a better understanding of the interaction between membrane inclusions.