Surfactant stabilized water/oil/water (w/o/w) double emulsions have received much attention in the last years motivated by their wide applications. Among double emulsions, those stabilized by phospholipids present special interest for their imitation of artificial cells, allowing the study of the effect of confining chemical reactions in biomimetic environments. Upon evaporation of the oil shell, phospholipid stabilized double emulsions can also serve as templates for giant vesicles. In this context, general assumptions have been made on the self-assembly and structural organization/arrangement of amphiphilic molecules, at the aqueous/oil liquid interface. However, to the best of our knowledge, no detailed evidence of the interfacial structuring have been reported. In this paper, w/o/w double emulsions formulated using the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and a mixture of chloroform and cyclohexane as the oil phase were produced using a microfluidic device. To obtain information on the phospholipid arrangement, the w/o/w interface was investigated by spatially resolved micro-focusing SAXS. We observed that (i) the basic units forming both the w/o and o/w interfaces were oil-swollen DMPC bilayers, arranged into a substantially disordered shell of $45 mm thickness surrounding the internal oil phase; (ii) the evaporation process was slow, i.e. in the order of one hour at 50 C and (iii) oil evaporation led to a shrinkage of the interfacial shell, but not to an increase of the ordering of the lipid bilayers. Interestingly, no stacked DMPC bilayers were observed during the evaporation process, as shown by the absence of Bragg's peaks in the SAXS intensity profiles.