We report the structural and mechanical behavior of multicomponent hydrogels comprising the commercial poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) block copolymer F127 and alginate. Previous studies on this system have shown thermoreversible behavior in shear rheology. Here we explore the properties of these materials under compression and large deformations, relevant to applications such as wound dressings that require mechanical robustness. For gels with lower F127 concentration, we find that the stiffness of the gels can be ascribed to the alginate network, and that the Young's modulus and fracture stress do not strongly depend on temperatures. However, for gels with an F127 concentration of 30 wt %, the Young's modulus is enhanced at higher temperatures. Under large deformations, the fracture stress and fracture strain of the materials can be independently varied using the alginate and F127 concentrations, respectively; without the trade‐off in these properties that is often observed in rigid polymer networks. Small‐angle X‐ray scattering shows a power‐law dependence scattering intensity on q arising from the alginate network and scattering peaks consistent with rearranging micelles. For gels with lower F127 concentrations, we find a disordered–body‐centered cubic (BCC)‐face‐centered cubic (FCC) progression of states with temperature, and a BCC/FCC mixture for gels with higher F127 concentrations.