Recent magnetometry measurements in modulation-doped ${\text{La}}_{1\ensuremath{-}x}{\text{Ca}}_{x}{\text{MnO}}_{3}$ suggested that a net magnetization extends from the ferromagnetic layers into the adjacent antiferromagnet layers. Here we test this hypothesis by polarized neutron reflectometry, which allows us to determine the depth resolved magnetization profile. From fits to the reflectivity data we find that the additional magnetization does not occur at the ferromagnetic/antiferromagnetic interfaces, but rather in a thin region of the first antiferromagnetic layer adjacent to the interface with the substrate.