Two constructions are studied that are inspired by the ideas of a recent paper by the authors. The diagonal complex D and its barycentric subdivision BD related to an oriented surface of finite type F equipped with a number of labeled marked points. This time, unlike the paper mentioned above, boundary components without marked points are allowed, called holes. The symmetric diagonal complex D inv and its barycentric subdivision BD inv related to a symmetric (=with an involution) oriented surface F equipped with a number of (symmetrically placed) labeled marked points. The symmetric complex is shown to be homotopy equivalent to the complex of a surface obtained by “taking a half” of the initial symmetric surface.