The department and a municipality may designate and establish controlled-access highways as new and additional facilities, or may designate and establish an existing highway as included within a controlled-access facility. The department and the municipality may provide for the elimination of an intersection at grade of a controlled-access facility with an existing highway by grade separation or service highway, or by closing off the highway at the right-of-way boundary line of the controlled-access facility. After the establishment of a controlled-access facility, a highway not part of the facility may not intersect it at grade. A municipal or state highway, or other public way, may not be opened into or connected with a controlled-access facility without the consent and prior approval of the department or the municipality having jurisdiction over the controlled-access facility. The department shall give its consent and approval only if the public interest is served.