Block copolymers assembled into micelles have gained a lot of attention to improve drug delivery. The recent drawbacks of the poly(ethylene oxide) blocks (PEO) contained in amphiphilic pluronics derivatives made of a central poly(propylene oxide) block surrounded by two PEO blocks were recently revealed, opening the way to the design of new amphiphilic block copolymers able to self-assemble in water and to entrap molecules of interest. Here, a family of p(methyloxazoline)-b-p(tetrahydrofuran)-b-p(methyloxazoline) triblock copolymers (called TBCP) is synthesized using cationic ring opening polymerization. Studies of micelle formation using dynamic light scattering, isothermal titration calorimetry (ITC), NMR diffusion-ordered spectroscopy (DOSY), and fluorescence experiments lead us to draw a relationship between copolymer structure and the physicochemical properties of the block copolymers (critical micellar concentration (CMC), Nagg, core diameter, shell thickness, etc.). The packing parameter of the block copolymers indicates the formation of a core–corona structure. Hydrosolubilizing properties of TBCPs were exemplified with curcumin selected as a highly insoluble drug model. Curcumin, a natural polyphenolic compound, has shown a large spectrum of biological and pharmacological activity, including anti-inflammatory, antimicrobial, antioxidant, and anticarcinogenic activities. An optimized formulation process reveals that the aggregation number is the parameter affecting drug encapsulation. Patch clamp experiments carried out to study the interaction of TBCP with the cell membrane demonstrate their permeation property suitable to promote the cellular internalization of curcumin.