The assembly of two-dimensional cyanide-bridged Fe(III)-Ni(II) square grid networks at the air-water interface and subsequent transfer of these networks as isolated monolayer, isolated bilayer, and multiple bilayer (multilayer) films via the Langmuir-Blodgett technique results in novel low-dimensional systems in which the effects of dimensionality on magnetic behavior in molecule-based materials can be observed. The magnetic response of these films between 2 < T < 300 K in dc fields from -50 < H < 50 kG and in 4 G ac fields from 1 Hz to 1 kHz are reported. The results show the presence of ferromagnetic domains with characteristic hysteresis in each of the three systems. The magnetic response for all three samples is anisotropic with a stronger field-cooled magnetization observed when the planes of the films are aligned parallel to the applied field. Additionally, each of the three samples shows frequency dependence in both the real and imaginary components of the ac susceptibility. This behavior is interpreted as being characteristic of spin glass-type ordering of ferromagnetic domains to form a cluster glass. A lower glass temperature (T(g)) is observed in the isolated monolayer film relative to the bilayer and multilayer samples. The bilayer sample shows two glass transitions at T(g1) = 3.8 K and T(g2) = 5.4 K, whereas only one transition at T(g) = 5.4 K is observed in the multilayer sample. The different magnetic responses of the three films are attributed to different in-plane, interplane, and long-range dipolar exchange interactions.