This study aimed to apply the distribution of relaxation times (DRT) analysis on impedance spectra to model the electrochemical circuit of the electrode’s surface and reveal information about charge transfer, mass transport, and surface kinetics. A Cu-BTC metal–organic framework was synthesized and mixed with graphite to create a semiconductor layer on top of a glassy carbon electrode (GCE). Electrochemical impedance spectroscopy was applied to determine the effect of Cu-BTC thickness and Cu-BTC@Graphite mixing ratio, both compressed onto a graphite electrode. Cu-BTC acts as an insulator, thus it greatly reduces the conductivity of the electrode. An optimal ratio is observed at 60% Cu-BTC@Graphite. Cu-BTC@Graphite in a polymer mixture was drop-casted onto the GCE. Gold nanoparticles were electrodeposited, and the thiolated aptamer was immobilized via the Au-S bond formation. The impedance spectra were obtained for the hybrid nanomaterial electrode assembly. DRT plots were generated using pyDRTtools, showing 4-5 characteristic peaks from bare GCE to 3 characteristic peaks after modification. The Python package “Impedance.py” was used to fit the EIS data to each proposed equivalent circuit model (ECM) for the final assembly. Out of the six proposed ECMs, the Randles circuit with constant phase element (CPE) and a custom circuit with transmission line model (TLM) showed the best fit with root mean square error of 11.0 and 8.0, respectively. TLM applies to porous electrodes with high surface area, while the CPE accounts for the non-ideal capacitive behavior of the double layer, which is common in most biosensors.