The surface-confined formation of bicomponent organic molecular networks providing open pores following hierarchic assembly principles is investigated by low-temperature scanning tunneling microscopy and ab initio theoretical methods. The nanomeshes are realized by codeposition of N,N′-diphenyl oxalic amide and sexiphenyl dicarbonitrile molecules, with the substrate held at room temperature and subsequent cooling to cryogenic temperatures. We find that the formation of mixed molecular networks is generally preferred over phase segregation. Depending on the exact stoichiometry of the constituents, different types of open networks self-assemble on the employed Ag(111) surface. All network types reflect hierarchic architectures, where essential molecular interactions are identical and the noncovalent bonding of sexiphenyl to oxalic amide molecules prevails. The different association motifs are assessed by theoretical modeling to unravel the mechanisms mediating the hierarchic organization, whereby a cooperative binding energy enhancement represents a significant factor.