We present a systematic investigation of the series of compounds FexCo1-xNb2O6 by means of x-ray and neutron powder diffraction combined with magnetic measurements, carried out in the paramagnetic as well as in the ordered state, to probe the stability of the magnetic ordering against the composition changes in this model Ising system. Fe for Co substitution induces a continuous lattice volume increase, preserving the orthorhombic crystal structure. The unit-cell expansion is anisotropic and occurs mainly in the ab plane. The observed magnetic structures for x=0,0.8, and 1 are described by the propagation vectors (0,1/2,0) and (1/2,1/2,0), and are consistent with the picture of ferromagnetic Ising-type chains of Fe/Co spins antiferromagnetically coupled by weak interchain interactions. We find out that for 0