For version 9 (and possibly older versions), you can use
Inner[Composition[Defer, Times], {{1, 2}, {3, 4}}, {{5, 6}, {7, 8}}, Composition[Defer, Plus]]] // MatrixForm or
Inner[Defer[Times@##] &, {{1, 2}, {3, 4}}, {{5, 6}, {7, 8}} ,Defer[Plus@##] &]] // MatrixForm or
Inner[Composition[HoldForm, Times], {{1, 2}, {3, 4}}, {{5, 6}, {7, 8}}, Composition[HoldForm, Plus]]] // MatrixForm to get
