Dust storms are typical dispersed two-phase atmospheric turbulence involving electrified charged dust particles. Previous observations have demonstrated that clean-air atmospheric turbulence is strongly intermittent. However, the intermittency of the wind velocity, concentration of dust particles with a diameter smaller than
$10\ \mathrm {\mu }{\rm m}$
(PM10) and electric fields, known as multifield intermittency, has not been reported or characterized yet. Here, we quantify the small-scale multifield intermittency of dust storms using datasets obtained from the Qingtu Lake Observation Array and a wavelet-based data analysis technique. The results indicate that the probability density functions of the multifield increments are scale dependent, and the scaling exponents of the multifield structure functions exhibit anomalous scaling, suggesting that the multiple fields in dust storms are also highly intermittent. Specifically, the wind velocity during dust storms appears to be more intermittent as compared with clean-air conditions. Among the multiple fields, the small-scale intermittency is strongest for PM10 dust concentration, moderate for electric fields and weakest for wind velocity. Furthermore, the anomalous scaling of multiple fields is well described by the hierarchical structure theory of turbulence. It is theoretically predicted that the wind velocity displays a one-dimensional filamentary structure, while the PM10 dust concentration and electric fields display two-dimensional sheet-like structures. Finally, after removing the coherent components of the observed time series by the proposed wavelet conditioning statistics, Kolmogorov linear scaling is recovered for the multiple fields, suggesting that small-scale multifield intermittency is caused by the presence of small-scale coherent structures.