Abstract We present the joint Chandra, XMM-Newton, and NuSTAR analysis of two nearby Seyfert galaxies, NGC 3081 and ESO 565-G019. These are the only two having Chandra data in a larger sample of 10 low-redshift (z ≤ 0.05), candidates Compton-thick (CT) Active Galactic Nuclei selected in the 15–150 keV band with Swift-BAT that were still lacking NuSTAR data. Our spectral analysis, performed using physically motivated models, provides an estimate of both the line-of-sight (l.o.s.) and average (N _H,S ) column densities of the two torii. NGC 3081 has a Compton-thin l.o.s. column density N _H,z = [0.58–0.62] × 10²⁴ cm⁻², but the N _H,S , beyond the CT threshold (N _H,S = [1.41–1.78] × 10²⁴ cm⁻²), suggests a “patchy” scenario for the distribution of the circumnuclear matter. ESO 565-G019 has both CT l.o.s. and N _H,S column densities (N _H,z > 2.31 × 10²⁴ cm⁻² and N _H,S > 2.57 × 10²⁴ cm⁻², respectively). The use of physically motivated models, coupled with the broad energy range covered by the data (0.6–70 keV and 0.6–40 keV, for NGC 3081 and ESO 565-G019, respectively) allows us to constrain the covering factor of the obscuring material, which is C _TOR = [0.63–0.82] for NGC 3081, and C _TOR = [0.39–0.65] for ESO 565-G019.