The Jevons group is an isometry group of the Hamming metric on the -dimensional vector space over (2). It is generated by the group of all permutation ( × )-matrices over (2) and the translation group on . Earlier the authors of the present paper classified the submetrics of the Hamming metric on for ⩾ 4, and all overgroups of which are isometry groups of these overmetrics. In turn, each overgroup of is known to define orbital graphs whose “natural” metrics are submetrics of the Hamming metric. The authors also described all distance-transitive orbital graphs of overgroups of the Jevons group . In the present paper we classify the distance-transitive orbital graphs of overgroups of the Jevons group. In particular, we show that some distance-transitive orbital graphs are isomorphic to the following classes: the complete graph , the complete bipartite graph , the halved ( + 1)-cube, the folded ( + 1)-cube, the graphs of alternating forms, the Taylor graph, the Hadamard graph, and incidence graphs of square designs.