Liquid-liquid phase separation (LLPS) has been proposed as a primitive compartmentalization mechanism at the origin of life. One major class of LLPS systems are complex coacervates, which have been assembled in the laboratory from potentially available biopolymers on early Earth such as peptides and nucleic acids. Such primitive coacervates have shown prebiotically relevant functions such as compartmentalization, scaffolding, and catalysis. However, how primitive coacervates could increase their structural complexity has not yet been well studied. Here, as a demonstration of a plausible mechanism by which primitive coacervate droplets can increase their structural complexity, we assembled and characterized a peptide-DNA coacervate droplet consisting of multiple co-assembled phases, in this case, a liquid crystal (LC) phase. LC phases in particular have been shown to promote chemical scaffolding and reaction selectivity, and we observed that the assembly of a LC-coacervate could be governed by prebiotically available environmental processes such as dehydration/rehydration or heat cycles. Structural complexity acquisition from LC phases could enhance the ability of primitive compartments to undergo selective molecular evolution.