Lattice resonances are collective modes supported by periodic arrays of nanostructures. They originate from the coherent interaction between the localized modes of the individual constituents of the array, which, for systems made of metallic nanostructures, usually correspond to the electric dipole plasmon. Unfortunately, fundamental symmetry reasons preclude a two‐dimensional (2D) arrangement of electric dipoles from absorbing more than half the incident power, thus imposing a strong limitation on the performance of conventional lattice resonances. This work introduces an innovative solution to overcome this constraint, which is based on using an array made of a unit cell containing one metallic and one dielectric nanostructure. Using a rigorous coupled dipole model, it is shown that this system can support two independent lattice resonances associated, respectively, with the electric and magnetic dipole modes of the nanostructures. By adjusting the geometrical characteristics of the array, these two lattice resonances can be meticulously aligned in the spectral domain, leading to the total absorption of the incident power. The results of this work provide clear, yet general, guidelines for the rational design of arrays sustaining lattice resonances capable of producing perfect absorption, thus leveraging the potential of these modes for applications requiring an efficient absorption of light.