A one-to-two disjoint-path cover of a graph G is a pair (P₁, P₂) of two vertex-disjoint paths that connect one source to two sinks in G and span G. It is called ε-balanced if |ℓ(P₁)−ℓ(P₂)|=ε, where ℓ(P₁) and ℓ(P₂) denote the lengths of paths P₁ and P₂, respectively. The matching composition network is a family of interconnection networks, each of which connects two components with the same number of vertices by a perfect matching. This paper addresses some properties about one-to-two disjoint-path covers of matching composition networks. Applying the proposed main theorem, a one-to-two ε-balanced disjoint-path cover in some well-known interconnection networks, such as crossed cubes, twisted cubes, locally twisted cubes, etc., can be easily obtained for a given odd integer ε.