Let Γ be a distance-semiregular graph on Y , and let D Y be the diameter of Γ on Y . Let Δ be the halved graph of Γ on Y . Fix x ∈ Y . Let T and T ′ be the Terwilliger algebras of Γ and Δ with respect to x , respectively. Assume, for an integer i with 1 ≤ 2 i ≤ D Y and for y , z ∈ Γ 2 i ( x ) with ∂ Γ ( y , z ) = 2 , the numbers | Γ 2 i - 1 ( x ) ∩ Γ ( y ) ∩ Γ ( z ) | and | Γ 2 i + 1 ( x ) ∩ Γ ( y ) ∩ Γ ( z ) | depend only on i and do not depend on the choice of y , z . The first goal in this paper is to show the relations between T -modules of Γ and T ′ -modules of Δ . Assume Γ is the incidence graph of the Hamming graph H ( D ,  n ) on the vertex set Y and the set C of all maximal cliques. Then, Γ satisfies above assumption and Δ is isomorphic to H ( D ,  n ). The second goal is to determine the irreducible T -modules of Γ . For each irreducible T -module W , we give a basis for W the action of the adjacency matrix on this basis and we calculate the multiplicity of W .