Albosta was born in Saginaw, Michigan and attended Saginaw and Chesaning public schools. He graduated from Chesaning Agricultural School, and attended Delta College in Bay City. He served in the United States Navy, was a farmer, owner, and developer of Misteguay Creek Farms. He served as Albee Township Trustee and was associate director of the Saginaw County Soil Conservation District. He was Saginaw County Commissioner, 1970-1974 and served in the Michigan State House of Representatives, 1974-1976, representing the 86th District. In 1976, he first ran for the United States House of Representatives, losing to incumbent Elford Cederberg.

In 1978, Albosta unseated the incumbent Cederberg and was elected as a Democrat from the 10th District to the Ninety-sixth Congress and to the two succeeding Congresses, serving from January 3, 1979 to January 3, 1985. He was an unsuccessful candidate for reelection to the Ninety-ninth Congress, losing to Bill Schuette. He also ran unsuccessfully against Schuette in 1986. Albosta is a resident of St. Charles, Michigan.

Albosta was chair of the House Subcommittee on Human Resources which conducted an investigation into the so-called October Surprise, in which the presidential campaign of Ronald Reagan was alleged to have orchestrated delaying the release of U.S. hostages held by Iran until after the election as well as allegations that the Reagan campaign stole President Carter's briefing materials. The subcommittee's final report in 1984 excoriated Reagan's campaign staff for employing unethical, if not illegal tactics.

His daughter, Christine C. White, was appointed in March 2003 as the Director of Agriculture Policy for the Michigan Department of Agriculture.