Historically, biblical covenants tended to apply first to families and then, as those families expanded into nations, to those nations. So, the family and household applications of these covenants are explicit in their foundational language and context. This was even true of the Mosaic covenant, which God made with “the house of Jacob” and literally the “sons” of Israel (Ex. 19:3). These names emphasized family over nationhood, perhaps because, as escapees from Egypt, Israel wasn’t yet a recognized nation.
God often deals with His entire covenant people as a unified whole, often based on their actions as a whole or on those of a representative few. He rescued His entire covenant people (only eight people) from the flood in Noah’s day because Noah found favor (Gen. 6:8), just as He rescued all Israel from Egypt when His people cried out (Ex. 2:23–25). He punished Israel for Achan’s sin because He treated Achan as representing the nation (Josh. 7:1; 22:20).
God also deals with households as a unified whole. When He identified Isaac as Abraham’s covenant heir (Gen. 17), He required every male in the household to be circumcised (including Ishmael, whom He rejected as Abraham’s heir). During Israel’s rescue from Egypt, each household’s Passover observance saved its firstborn from death (Ex. 12). When Achan was found out, Israel restored their standing with God by destroying his entire household (Josh. 7:24–26).