We have used directed two-component self-assembly to "pattern" organic monolayers on the nanometer scale at the liquid/solid interface. The ability of the scanning tunneling microscope to investigate structural details in these adlayers was used to gain insight into the two-component two-dimensional phase behavior. The components are symmetrically alkylated bisurea derivatives (R1-urea-spacer-urea-R2; R1, R2=alkyl, spacer=alkyl or bisthiophene). The bisthiophene unit acts as a marker and its bisurea derivative (T2) is a component in all the mixtures investigated. By varying the position of the hydrogen-bond forming urea groups along the molecule and the length of the alkyl chains of the other components, the effect of 1) hydrogen bonding, 2) molecule length, 3) odd-even effects, and 4) shape complementarity on the two-dimensional phase behavior was investigated. Insight into the effect of these parameters leads to the control of the two-dimensional patterning: from randomly intermixed systems to phase separation.