In order to investigate the magnetic phase transition that occurs at the Curie temperature in magnetic thin- and ultrathin-film multilayers, we have carried out extensive magnetization measurements in the temperature range embracing the critical region on amorphous (Tb_0.27Dy_0.73)_0.32Fe_0.68 thin- and ultrathin-film multilayers separated by magnetic (Cr) or non-magnetic (Nb) interlayers. These data are analyzed by using the conventional methods like the modified Arrott plots, Kouvel-Fisher method, scaling-equation-of-state analysis and the magnetization isotherm at the Curie point and the critical exponents β, γ and δ which describe the phase transition based on the power laws of the spontaneous magnetization, the initial susceptibility and the critical magnetization isotherm, respectively, have been deduced. Depending on the type of the sample, we could see two types of transitions, either characterized by three-dimensional Heisenberg-like critical exponents or two-dimensional Ising-like. The reasons for this are discussed in detail.