To simulate amphiphilic polymers, we introduce an extended hydrophobic/hydrophilic (HP) model which, in contrast to the standard "beads-on-a-string" HP model, incorporates the dualistic nature of monomer units, each consisting of hydrophobic (H) and hydrophilic (P) interaction sites. For this coarse-grained model, the hydrophobically driven conformational transitions are studied using extensive molecular dynamics simulations. We find that, depending on the interaction between H and P sites, a variety of thermodynamically stable anisometric chain morphologies are possible in a solvent selectively poor for H sites, including disklike structures, stretched strings of intramolecular micelles, and cylindrical-shaped conformations. These microstructures are formed due to intramolecular segregation of chemically different H and P groups. Under certain conditions, the chain size R-g as a function of solvent quality can behave in a nonmonotonic manner, showing an increase when the solvent becomes poorer for hydrophobic sites. For the range of the chain lengths N simulated (N less than or equal to 1024), the formation of highly anisotropic conformations can lead to the Rg proportional to N0-9 scaling.