Experimental and theoretical lifetimes ${\ensuremath{\tau}}_{{v}^{\ensuremath{'}}{N}^{\ensuremath{'}}}$ for $e{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ and $d{}^{3}{\ensuremath{\Pi}}_{u}^{\ensuremath{-}}$ states of molecular hydrogen and deuterium are presented in a wide range of vibrational ${v}^{\ensuremath{'}}$ and rotational ${N}^{\ensuremath{'}}$ quantum numbers. Lifetimes have been measured by a delayed coincidence method following electron-impact excitation from the ground state. The cascade effects on the lifetimes measured were estimated to be negligible through a detailed analysis. Predissociative rates were estimated by the Fermi golden rule based on adiabatic rovibronic wave functions and radial coupling matrix elements $B(R)$ for the $e{}^{3}{\ensuremath{\Sigma}}_{u}^{+}\ensuremath{\sim}b{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ and $d{}^{3}{\ensuremath{\Pi}}_{u}^{\ensuremath{-}}\ensuremath{\sim}c{}^{3}{\ensuremath{\Pi}}_{u}^{\ensuremath{-}}$ pairs of interacting states. The radiative lifetimes of both excited states were evaluated by the theoretical $e{}^{3}{\ensuremath{\Sigma}}_{u}^{+}\ensuremath{-}a{}^{3}{\ensuremath{\Sigma}}_{g}^{+}$ and $d{}^{3}{\ensuremath{\Pi}}_{u}--a{}^{3}{\ensuremath{\Sigma}}_{g}^{+}$ transition dipole moment functions $d(R)$ and adiabatic rovibronic wave functions of the states involved. The electronic matrix elements $B(R)$ and $d(R)$ were obtained by direct ab initio calculations as well as within the framework of quantum defect theory. The ab initio $B(R)$ functions were calculated by the finite-difference method and by the analytical Sidis formula, which were based on the full configuration-interaction electronic wave functions. At small and medium internuclear distances the quantum defect matrix elements agree well with their ab initio counterparts. The predissociative rates for both $e{}^{3}{\ensuremath{\Sigma}}_{u}^{+}{(v}^{\ensuremath{'}}>~0)$ and $d{}^{3}{\ensuremath{\Pi}}_{u}^{\ensuremath{-}}{(v}^{\ensuremath{'}}>~4)$ states of hydrogen were found to increase sharply as the ${v}^{\ensuremath{'}}$ value of the predissociated level increases, and become compatible with the radiative decay rate. The predissociation effect in the deuterium was negligible for both states studied; hence their experimental lifetimes correspond to the radiative decay channel only. A sum of the theoretical radiative and predissociative rates was in good agreement with the experimental results for the $e{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ state but slightly overestimated for the $d{}^{3}{\ensuremath{\Pi}}_{u}^{\ensuremath{-}}$ state. Reasons for the remaining discrepancies are discussed and suggestions for further improvements are given.