The self-assembly of 1,3,5-benzenetribenzoic acid (BTB) molecules on both Cu(111) and epitaxial graphene grown on Cu(111) were studied by scanning tunneling microscopy (STM) and, low-energy electron diffraction (LEED) under ultrahigh vacuum conditions. On Cu(111), the BTB molecules were found to mainly arrange in close-packed structures through H-bonding between the (partially) deprotonated carboxylic acid groups. In addition, porous structures formed by intact BTB molecules-and also based on H-bonding-were observed. On graphene grown on Cu(111) the BTB molecules mainly form porous structures accompanied by small patches of disordered close-packed structures. Upon annealing, BTB adsorbed on Cu(111) is fully deprotonated and arranges in the close-packed structure while in contrast on graphene/Cu(111) the porous network is exclusively formed. This shows that the molecular self-assembly behavior is highly dependent on the first substrate layer: one graphene layer is sufficient to considerably alter the interplay of molecule substrate and intermolecular interactions in favor of the latter interactions.