Motivated by observations of the heterogeneous domain structure on the surface of cells and vesicles and by domain formation due to the adsorption of complex molecules onto composite membranes, we consider a minimal quasi-2D model to describe the structure of binary mixtures on the surface of a spherical particle. We study the effect of miscibility and adsorbing particle (AP) addition on the mixture structure. We define a new scalar quantity, the geodesic mixing parameter Ξ, through which we detail the effect of miscibility and the role of preferential affinity of APs with one of the two components of the mixture, distinguishing unambiguously between mixing and demixing solely induced by APs. Finally, by inspecting the distributions of void sizes, we show how void formation is ruled by miscibility and AP-mixture interactions, which control the transition from exponentially tailed to fat-tailed distributions.