My father-in-law left his home to his two sons, one being my husband. My husband's brother purchased my husband's half from him. Will my husband owe any type of taxes on the money from the house?

He may. It depends on the appraised value of the house and what he paid for it. The estate should appraise the property and determine its value at the time the father died. If his brother paid more than 1/2 that value for his share, then he may owe taxes on that difference.