We design sterically stable biocompatible vehicles with tunable shapes through the self-assembly of a binary mixture composed of amphiphilic molecular species, such as PEGylated lipids, and phospholipids under volumetric confinement. We use a molecular dynamics-based mesoscopic simulation technique called dissipative particle dynamics to resolve the aggregation dynamics, structure, and morphology of the hybrid aggregate. We examine the effect of confinement on the growth dynamics and shape of the hybrid aggregate, and demonstrate the formation of different morphologies, such as oblate and prolate shaped vesicles and bicelles. We perform these investigations by varying the degree of nanoscale confinement, for different relative concentrations of the species and the length of the functional groups. Results from our investigations can be used for the design and prediction of novel hybrid soft materials for applications requiring the encapsulation of therapeutic agents in micro- or nanofluidic channels.