A comprehensive elastic- and inelastic-neutron-scattering study of the binary mixed antiferromagnet Rb2Mn0.5Ni0.5F4 has been carried out. The pure materials, Rb2MnF4 and Rb2NiF4 are [2d] near-Heisenberg antiferromagnets of the K2NiF4 type. Elastic-scattering experiments demonstrate that the Mn++ and Ni++ ions are randomly distributed on a plane square lattice. At ∼ 64 K the system undergoes a second-order phase transition to two distinct [3d] antiferromagnetic structures, with both structures being composed of simple [2d] square antiferromagnetic arrays. All properties are found to be determined by the intraplanar interactions alone. Inelastic measurements show that at low temperatures the spin dynamics of this binary random alloy are characterized by two well-defined bands of excitations. The widths and energies of the zone-boundary modes are accurately predicted using a simple Ising cluster model while the over-all dispersion is correctly given by the Walker mean-crystal model. The above calculations involve only interaction constants taken from the pure materials and JMn-Ni=(JMn-MnJNi-Ni)1/2 so that there are no adjustable parameters. At higher temperatures it is found that the gap at q=0 renormalizes like the sublattice magnetization while the excitations at larger wave vectors remain well defined through TN and only slightly renormalized from their T=0 energies. Critical scattering measurements of the staggered susceptibility and the correlation length have been carried out between 69 and 120 K; it is found that over this temperature range they exhibit approximate power-law divergences with exponents close to those of the [2d]-Ising model.