We use soft x-ray vector-ptychographic tomography to determine the three-dimensional magnetization field in superparamagnetic nanoparticles self-assembled at the liquid-liquid interface and reveal the magnetic order induced by layered structure. The spins in individual nanoparticles become more aligned with increasing number of layers, resulting in a larger net magnetization. Our experimental results show a magnetic short-range order in the monolayer due to the proliferation of thermally induced magnetic vortices and a magnetic long-range order in the bilayer and trilayer, stemming from the strengthened dipolar interactions that effectively suppress thermal fluctuations. We also observe a screening effect of magnetic vortices and the attractive interaction between the magnetic vortices with opposite topological charges. Our work demonstrates the crucial role of layered structure in shaping the magnetization of nanoparticle assemblies, providing new opportunities to modulate these properties through strategic layer engineering.