Abstract Effective transport properties of two biocompatible nanofibrous membranes—gelatin and chitosan—were evaluated using the gas transport measurement. The assessments involve the counter-current diffusion carried out both in Graham's and Wicke-Kallenbach cells under isothermal steady-state conditions. Additionally, the isothermal quasi-stationary gas permeation was also performed in modified Wicke-Kallenbach cell. It was found that the obtained transport characteristics reflect the gas transport mechanism which takes place predominantly in the continuum regime due to the prevailing macroporosity of the electrospun nanofibrous membranes. The gas permeation transport characteristics were evaluated from permeation cell measurements carried out at low pressures. The actual transport mechanism corresponded to the Knudsen flow dominating over continuous flow. The accuracy of the transport characteristics was estimated as the 95% confidence regions. It was confirmed that the confidence region shape of the optimized transport characteristics was intimately connected with the prevailing mass transport mechanism.