The interaction of a bovine serum albumin (BSA) protein with the mixture of anionic sodium dodecyl sulfate (SDS) and cationic dodecyltrimethylammonium bromide (DTAB) has been investigated by small-angle neutron scattering (SANS) and dynamic light scattering (DLS). Both SDS and DTAB as individuals interact electrostatically as well as hydrophobically with BSA and form connected protein-decorated micelle like complexes in the aqueous solution, in which the well-defined surfactant micelles are organized along the randomly distributed unfolded polypeptide chain of the protein. The protein-surfactant interaction has been tuned by adding different molar mixtures of SDS and DTAB in BSA aqueous solution. It is found that a lower molar fraction of either surfactant in the protein-mixed surfactant complexes results in the formation of a connected protein-decorated micelle structure similar to those of pure surfactants. As the molar fraction of one of the surfactants in the mixture approaches the equimolar fraction, the structure formed by the protein-mixed surfactant is very different from the connected protein-decorated micelle like structure. Different microstructures of BSA-mixed surfactant complexes are formed, mostly governed by the structure of mixed surfactants arising from the strong electrostatic interaction of oppositely charged components. In this case, unfolded proteins wrap the structures of mixed surfactants around their surface. Along with the connected protein-decorated micelle like structure, rod-like and bilayer vesicles of protein-surfactant complexes are formed at different molar fractions of mixed surfactants.