Thermoplastic elastomer SEBS, a triblock copolymer composed of styrene (S) and ethylene-co-butylene (EB) blocks, can be dissolved and processed by electrospinning to produce flexible nonwoven mats that can be interesting for applications like filtration or separation membranes. Controlling surface properties such as hydrophobicity/hydrophilicity is critical to achieving a desired performance. In this study, hydrophobic electrospun SEBS mats were obtained, following which an amphiphilic molecule (Pluronic F127) was solution-blended with SEBS prior to electrospinning, in a bid to produce a hydrophilic membrane. The result was a fast-spreading superhydrophilic mat with thinner fibers that preserved the flexibility of the SEBS. The morphologies of nonwoven mats, flat films (prepared by dip-coating using identical solutions) and of the surface of individual fibers were characterized using different microscopy techniques (optical, scanning electron microscopy and atomic force microscopy). Chemical analysis by X-ray photoelectron spectroscopy (XPS) revealed a large F127 concentration in the outermost surface layer. In addition, an analysis of dip-coated flat films revealed that for 20 wt % of F127, there was a change in the blend morphology from dispersed F127-rich regions in the SEBS matrix to an interconnected phase homogeneously distributed across the film that resembled grain boundaries of micellar crystals. Our results indicated that this morphology change at 20 wt % of F127 also occurred to some extent in the electrospun fibers and this, combined with the large surface area of the mats, led to a drastic reduction in the contact angle and fast water absorption, turning hydrophobic electrospun mats superhydrophilic.