A study of the magnetic structure of the [NH2(CH3)2]n[FeIIIMII(HCOO)6]n niccolite-like compounds, with MII = CoII (2) and MnII (3) ions, has been carried out using neutron diffraction and compared with the previously reported FeII-containing compound (1). The inclusion of two different metallic atoms into the niccolite-like structure framework leads to the formation of isostructural compounds with very different magnetic behaviors due to the compensation or not of the different spins involved in each lattice. Below TN, the magnetic order in these compounds varies from ferrimagnetic behavior for 1 and 2 to an antiferromagnetic behavior with a weak spin canting for 3. Structure refinements of 2 and 3 at low temperature (45 K) have been carried out combining synchrotron X-ray and high-resolution neutron diffraction in a multipattern approach. The magnetic structures have been determined from the difference patterns between the neutron data in the paramagnetic and the magnetically ordered regions. These difference patterns have been analyzed using a simulated annealing protocol and symmetry analysis techniques. The obtained magnetic structures have been further rationalized by means of ab initio DFT calculations. The direction of the magnetic moment of each compound has been determined. The easy axis of the MII for compound 1 (FeII) is along the c axis; for compound 2 (CoII), the moments are mainly within the ab plane; finally, for compound 3 (MnII), the calculations show that the moments have components both in the ab plane and along the c axis.