We have extended a model of lipid molecules (monomers), polymerized via their polar groups to form macrolipids, in mixed lipid monolayers at the air-water interface. Because of thermal fluctuations in the monolayer, the macrolipids, although confined essentially to two dimensions, might cross themselves or other macrolipids (bond crossing), in the plane of the monolayer, via the space created dynamically "under" the molecular spacers (bonds) connecting adjacent monomers along a macrolipid. We have considered that twisted (short) bonds possess a degeneracy D > 1 and that extended (long) bonds can be bound to the air-water interface, or not. We have performed computer simulations for semidilute and dense cases of such systems and shown how order parameters and clique (cluster) sizes depend on degree of polymerization, monomer concentration and temperature. We suggest experiments that might establish whether bond crossing and interface binding actually occur.