This paper presents, for the first time, measurements of neutron transparency ratios for nuclei relative to C measured using the (e,en) reaction, spanning measured neutron momenta of 1.4 to 2.4 GeV/c. The transparency ratios were extracted in two kinematical regions, corresponding to knockout of mean-field nucleons and to the breakup of Short-Range Correlated nucleon pairs. The extracted neutron transparency ratios are consistent with each other for the two measured kinematical regions and agree with the proton transparencies extracted from new and previous (e,ep) measurements, including those from neutron-rich nuclei such as lead. The data also agree with and confirm the Glauber approximation that is commonly used to interpret experimental data. The nuclear-mass-dependence of the extracted transparencies scales as A^{alpha} with {alpha} = -0.289 {pm} 0.007, which is consistent with nuclear-surface dominance of the reactions.