The structure of the low-lying levels of $^{91,92,93,95,97}\mathrm{Nb}$ and $^{94}\mathrm{Mo}$ was investigated with the proton-stripping ($^{3}\mathrm{He}$, $d$) reaction on targets of $^{90,91,92,94,96}\mathrm{Zr}$ and $^{93}\mathrm{Nb}$. The incident energy was 30.9 MeV for the $^{91,92}\mathrm{Zr}$ and $^{93}\mathrm{Nb}$ reactions and 24.7 MeV for the $^{94,96}\mathrm{Zr}$ reactions. The $^{90}\mathrm{Zr}$ reaction was studied at both energies. The experimental angular distributions are compared with local zero-range distorted-wave Born-approximation calculations, and spin, parity, and spectroscopic factors are deduced. The extracted spectroscopic factors are used to establish the proton configurations of the target ground states. The observed levels and spectroscopic factors are compared with shell-model predictions based on an $^{88}\mathrm{Sr}$ core. A surprising deviation from results of the simple shell-model calculations is observed for the relative transfer strengths to the two lowest 2+ levels in $^{94}\mathrm{Mo}$.