EDITED TO ADD: The history of this bridge likely goes back to the military road, constructed by the army, to connect Fort Dearborn, in Chicago, to Fort Howard, near Green Bay. The names "Green Bay Road/Avenue/Trail" are still in use from Chicago to the Wisconsin-Illinois state line to Green Bay, most of them following the alignment of the original military road. (Most of the route has been signed by the State of Wisconsin as the Green Bay Ethnic Trail.)
According to Christopher Bessert, in 1926, when the US government took over management of the federal highway system and implemented today's familiar numbering scheme, US-141 was designated to connect Milwaukee and Green Bay along the Lake Michigan shore. The "1" shows it to be the offspring of its parent route, US-41, that connects Milwaukee to Green Bay along the west shore of Lake Winnebago.
When Manitowoc was bypassed in 1956 by rerouting US-141, this bridge obviously could not handle highway traffic. The referenced Rapids Road bridge was built, just a few yards to the south, to accommodate the new bypass. For more about the history of US-141, see Christopher Bessert's Wisconsin Highways website.)
Somewhere along the line, the road name was changed from Green Bay Road to Mill Road to commemorate the Manitowoc Rapids mill operated by the Klingholz family. (Thanks to the Manitowoc County Historical Society for that bit of information.)
(US-141 itself was bypassed when it was upgraded to a full freeway, just a mile west of here. Today, it is known as I-43 and little of US-141 still exists.)