Muheim emigrated to the United States from Switzerland in 1883 and began his career in Arizona by brewing beer for area miners for several years. He used profits from this operation to acquire real estate and erected the Muheim Block on Brewery Gulch. This building housed the Brewery Bar as well as a local stock exchange and the Edelweis Restaurant. Later he and several prominent Bisbee businessman founded the Miners & Merchants Bank on Main Street.
The Muheim Heritage House served as the family residence until 1975 when it was donated to the City of Bisbee. The house was restored by the Bisbee Council on the Arts & Humanities and opened as a museum in 1980.