For simulating hydrophobic-amphiphilic (HA) copolymers, we have developed a "side-chain" HA model in which hydrophilic (P) interaction sites are attached to hydrophobic (H) main chain, thereby forming amphiphilic (A) monomer units, each with dualistic (hydrophobic/hydrophilic) properties. Using this coarse-grained model, we performed molecular dynamics simulations of the hydrophobically driven self-assembly in a selective solvent, for both single-chain and multichain systems. The focus is on the regime in which H and P interaction sites are strongly segregated. Single-chain simulations are performed for copolymers with the same HA composition but with different distribution of H and A monomer units along the hydrophobic backbone, including regular copolymers comprising H and A units in alternating sequence, (HA)(x), regular multiblock copolymers (H(L)A(L))(x) composed of H and A blocks of equal lengths L = 3, and quasi-random proteinlike copolymers having quenched primary structure. In a solvent selectively poor for H sites, the proteinlike polyamphiphiles can readily adopt spherical-shaped compact conformations with the hydrophobic chain sections clustered at the globular core and the hydrophilic groups forming the envelope of this core and buffering it from solvent. Because of the fact that these globules are size- and shape-persistent objects, they maintain their morphological integrity even in rather concentrated solutions where no large-scale aggregation is observed. Moreover, we find that the population of aggregates generally decreases with worsening solvent quality. The compact conformations of long regular copolymers tend to be strongly elongated in one direction.