Phospholipid (PL) membranes are ubiquitous in nature and their phase behavior has been extensively studied. Lipids assemble in a variety of structures and external stimuli can activate a quick switch between them. Amphiphilic block copolymers (BCPs) can self-organize in analogous structures but are mechanically more robust and transformations are considerably slower. The combination of PL dynamical behavior with BCP chemical richness could lead to new materials for applications in bioinspired separation membranes and drug delivery. It is timely to underpin the phase behavior of these hybrid systems and a few recent studies have revealed that PL–BCP membranes display synergistic structural, phase-separation, and dynamical properties not seen in pure components. One example is phase-separation in the membrane plane, which seems to be strongly affected by the ability of the PL to form lamellar phases with ordered alkyl chains. In this paper we focus on a rather less explored design handle which is the crystalline properties of the BCP component. Using a combination of confocal laser scanning microscopy and X-ray scattering we show that hybrid membranes of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and methoxy-poly(ethylene glycol)-b-poly(ε-caprolactone) (mPEG-b-PCL) display BCP-rich and PL-rich domains when the BCP comprises crystalline moieties. The packing of the hydrophilic part of the BCP (PEG) favors mixing of DPPC at the molecular level or into nanoscale domains while semi-crystalline and hydrophobic PCL moieties bolster microscopic domain formation in the hybrid membrane plane.