We extend earlier work that gave exact results for the thermodynamics and size parameters of a confined polymer to the case where the monomers have complex structure. The only restriction on the complex monomers is that they be composed of a linear sequence of submonomers, each of which occupies one site on the lattice. The complex monomers can contain both rigid and flexible parts. For ease of understanding, we first treat a square (2-d) lattice. Then the cubic (3-d) lattice is treated. As before, the confining walls can be both chemically and physically rough, and the attraction energy of submonomers for the lattice sites can be different for each lattice site and importantly can be different for each submonomer. There is no restriction on the number of, or the linear sequencing of, the chemically different complex monomers that constitute a polymer chain. Our results have application to a confined polymer in solution as found in polymer chromatography as well as to adsorption/absorption of polymers onto/into nanoparticles. We demonstrate the ease of use and utility of the method by constructing a model of poly(p-phenylene), a semiconducting polymer, and demonstrate the transition from face-on to edge-on surface adsorption based upon the p-aromatic surface interaction, a phenomenon known to have impact on organic thin film transistor performance.