Liquid-liquid phase separation of biomacromolecules is crucial in various inter- and extracellular biological functions. This includes formation of condensates to control, e.g., biochemical reactions and structural assembly. The same phenomenon is also found to be critically important in protein-based high-performance biological materials. Here, we use a well-characterized model triblock protein system to demonstrate the molecular level formation mechanism and structure of its condensate. Large-scale molecular modeling supported by analytical ultracentrifuge characterization combined with our earlier high magnification precision cryo-SEM microscopy imaging leads to deducing that the condensate has a bicontinuous network structure. The bicontinuous network rises from the proteins having a combination of sites with stronger mutual attraction and multiple weakly attractive regions connected by flexible, multiconfigurational linker regions. These attractive sites and regions behave as stickers of varying adhesion strength. For the examined model triblock protein construct, the β-sheet-rich end units are the stronger stickers, while additional weaker stickers, contributing to the condensation affinity, rise from spring-like connections in the flexible middle region of the protein. The combination of stronger and weaker sticker-like connections and the flexible regions between the stickers result in a versatile, liquid-like, self-healing structure. This structure also explains the high flexibility, easy deformability, and diffusion of the proteins, decreasing only 10-100 times in the bicontinuous network formed in the condensate phase in comparison to dilute protein solution. The here demonstrated structure and condensation mechanism of a model triblock protein construct via a combination of the stronger binding regions and the weaker, flexible sacrificial-bond-like network as well as its generalizability via polymer sticker models provide means to not only understand intracellular organization, regulation, and cellular function but also to identify direct control factors for and to enable engineering improved protein and polymer constructs to enhance control of advanced fiber materials, smart liquid biointerfaces, or self-healing matrices for pharmaceutics or bioengineering materials.