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In some cases, a (weakly) exponential length\u2010attenuation, as in off\u2010resonant tunneling transport, extends to thicknesses even beyond 10\u00a0nm. This report deals with such charge transport characteristics observed in self\u2010assembled multilayers of the protein bacteriorhodopsin (bR). \u22487.5 to 15.5\u00a0nm thick bR layers are prepared on conductive titanium nitride (TiN) substrates using aminohexylphosphonic acid and poly\u2010diallyl\u2010dimethylammonium electrostatic linkers. Using conical eutectic gallium\u2010indium top contacts, an intriguing, mono\u2010exponential conductance attenuation as a function of the bR layer thickness with a small attenuation coefficient <jats:italic>\u03b2<\/jats:italic> \u2248 0.8 nm<jats:sup>\u22121<\/jats:sup> is measured at zero bias. Variable\u2010temperature measurements using evaporated Ti\/Au top contacts yield effective energy barriers of \u2248100 meV from fitting the data to tunneling, hopping, and carrier cascade transport models. The observed temperature\u2010dependence is assigned to the protein\u2010electrode interfaces. The transport length and temperature dependence of the current densities are consistent with tunneling through the protein\u2013protein, and protein\u2010electrode interfaces, respectively. 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