We study the relationship between postulation and reduction vectors of admissible multigraded filtrations F = [[[[F(n)]]]]n∈Zs of ideals in Cohen-Macaulay local rings of dimension at most two. This is enabled by a suitable generalization of the Kirby-Mehran complex. An analysis of its homology leads to an analogue of Huneke's fundamental lemma which plays a crucial role in our investigations. We also clarify the relationship between the Cohen-Macaulay property of the multigraded Rees algebra of F and reduction vectors with respect to complete reductions of F. © 2017 Rocky Mountain Mathematics Consortium.