We study the conformational behavior in a plane of a comb copolymer molecule, consisting of a semiflexible backbone and rigid side chains interacting via a van der Waals potential. Using a mean-field approach, two different regimes are distinguished depending on the strength of the attraction between the side chains. In the weak attraction limit the side chains are oriented preferably perpendicular to the backbone. The persistence length lambda of the comb copolymer molecule scales as the second power of the length of the side chain L: lambda is proportional to L2. In the strong attraction limit all side chains become strongly tilted and the persistence length scales as lambda is proportional to L4. The nonlinear bending regime is also studied and characterized by a change in structure and a decreasing moment of bending force as a function of curvature, i.e., bending becomes easier.