Micron-scale, liquid-liquid phase separation occurs in membranes of living cells, with physiological consequences. To discover which lipids might support phase separation in cell membranes and how lipids might partition between phases, miscibility phase diagrams have been mapped for model membranes. Typically, model membranes are composed of ternary mixtures of a lipid with a high melting temperature, a lipid with a low melting temperature, and cholesterol. Phospholipids in ternary mixtures are chosen primarily to favor stable membranes (phosphatidylcholines and sphingomyelins) or add charge (phosphatidylglycerols and phosphatidylserines). A major class of phospholipids missing from experimental ternary diagrams has been the phosphatidylethanolamines (PEs). PE-lipids constitute up to 20 mol% of common biological membranes, where they influence protein function and facilitate membrane fusion. These biological effects are often attributed to PE\'s smaller headgroup, which leads to higher monolayer spontaneous curvatures and higher melting temperatures. Taken alone, the higher melting points of saturated PE-lipids imply that liquid-liquid phase separation should persist to higher temperatures in membranes containing PE-lipids. Here, we tested that hypothesis by substituting a saturated PE-lipid (DPPE) for its corresponding PC-lipid (DPPC) in two well-studied ternary membranes (DOPC/DPPC/cholesterol and DiphyPC/DPPC/cholesterol). We used fluorescence microscopy to map full ternary phase diagrams for giant vesicles over a range of temperatures. Surprisingly, we found no micron-scale, liquid-liquid phase separation in vesicles of the first mixture (DOPC/DPPE/cholesterol), and only a small region of liquid-liquid phase separation in the second mixture (DiphyPC/DPPE/cholesterol). Instead, coexisting solid and liquid phases were widespread, with the solid phase enriched in DPPE. An unusual feature of these ternary membranes is that solid and liquid-ordered phases can be distinguished by fluorescence microscopy, so tie-line directions can be estimated throughout the phase diagram, and transition temperatures to the 3-phase region (containing a liquid-disordered phase, a liquid-ordered phase, and a solid phase) can be accurately measured.