2,4-Diamino-6-phenyl-1,3,5-triazines carrying one or two semiperfluorinated chains at the phenyl substituent have been investigated in binary mixtures with partially fluorinated benzoic acids by polarizing microscopy, differential scanning calorimetry, and X-ray diffraction. The number and positions of the fluorinated tails of the acid component were systematically modified. Equimolar mixtures of the triazines with the aromatic acids form discrete hydrogen-bonded heterodimers with an elongated central core. Mesomorphic properties are observed only if at least three terminal fluoroalkyl chains are grafted to the hydrogen-bonded rigid core. The dimeric supermolecules exhibit columnar mesophases with rectangular or oblique two-dimensional lattice symmetry or bicontinuous cubic phases. The mesophases of the dimers are ribbon phases resulting from the collapse of smectic layers. Thereby, the phase type is defined by the number and positions of the fluorinated tails of the two components. Docking of two or three equivalents of two-chain benzoic acids to the diaminotriazine core leads to the formation of cylindrical aggregates, which organize into hexagonal columnar phases, whereas 1:2 and 1:3 mixtures of the two-chain triazine with a three-chain fluorinated aromatic acid display micellar cubic phases.