Currently, tissue engineering technologies are promising for the restoration of damaged organs and tissues. For regeneration of electrically conductive tissues or neural interfaces, it is necessary to provide electrical conductivity for the transmission of electrophysiological signals. The developed biocomposite structures presented in this article possess such properties. Their composition includes bovine serum albumin (BSA), gelatin, eosin-Y and single-walled carbon nanotubes (SWCNTs). For the first time, a biocomposite structure was formed from the proposed hydrogel using a nanosecond laser, and a two-photon absorption cross section value of 580 GM was achieved. Increased viscosity over 3 mPa∙s and self-focusing with a nonlinear refractive index of 42 × 10⁻¹² cm²/W make it possible to create a biocomposite structure over the entire specified area. The obtained electrical conductivity value was 19 mS∙cm⁻¹, due to the formation of effective electrically conductive networks. For a biocomposite with a concentration of gelatin 3 wt. %, formed by low-energy near-IR pulses, the survival of Neuro 2A nerve tissue cells was confirmed. The obtained results are important for the creation of new tissue engineering structures and neural interfaces from a biopolymer hydrogel based on the organic dye eosin-Y and carbon nanotubes by two-photon polymerization.