The decays of the high-spin isomers of $^{178}\mathrm{Ta}$ (2.45 h) and $^{178}\mathrm{Lu}$ (23.8 min) to the two strongly admixed ${K}^{\ensuremath{\pi}}={8}^{\ensuremath{-}}$ states in $^{178}\mathrm{Hf}$ were reinvestigated. The main features of the previously reported decay schemes are confirmed and several long-standing ambiguities are resolved. The results of this investigation indicate that the 1147-keV level is largely the two-neutron state and the 1479-keV level is largely the two-proton state in $^{178}\mathrm{Hf}$. They are found to be 34% admixed with one another. This mixing value is in good agreement with the value deduced from the $\frac{M1}{E2}$ cascade ratios of the 1147-keV band and from the comparison of the $E1$ ($\ensuremath{\nu}=7$) hindrance factors of these two states in this mass region. The band-mixing matrix element for these two states was found to be in agreement with the recent theory which introduces the residual neutron-proton interaction to account for the mixing. The spin-parity of $^{178}\mathrm{Lu}^{m}$ (23.8 min) was deduced to be ${K}^{\ensuremath{\pi}}={9}^{\ensuremath{-}}$ with a possible Nilsson configuration of $\frac{9}{{2}^{\ensuremath{-}}}{[514]}_{p}$, $\frac{9}{{2}^{+}}{[624]}_{n}$.RADIOACTIVITY $^{178}\mathrm{Ta}^{m}$; from $^{175}\mathrm{Lu}(\ensuremath{\alpha}, n)$, $^{180}\mathrm{Hf}(p, 3n)$, and $^{181}\mathrm{Ta}(p, p3n)$; measured ${T}_{\frac{1}{2}}$, ${E}_{\ensuremath{\gamma}}$, ${I}_{\ensuremath{\gamma}}$; deduced $log\mathrm{ft}$. $^{178}\mathrm{Lu}^{m}$; from $^{176}\mathrm{Yb}(\ensuremath{\alpha}, np)$, measured ${T}_{\frac{1}{2}}$, ${E}_{\ensuremath{\gamma}}$, ${I}_{\ensuremath{\gamma}}$; deduced $log\mathrm{ft}$, $J$, $\ensuremath{\pi}$. Ge(Li) detectors, natural and enriched targets, ${E}_{\ensuremath{\alpha}}=46$ MeV and ${E}_{p}=33$ MeV.