"I have the privilege of worshiping in a small, family-integrated church. When asked about our various church programs, I explain that we are blessed with more than thirty different organizations to which our members belong — they are called families. I further explain that we have more than sixty youth directors — they are called parents. In fact, we have such a full schedule of events that there is a mandatory activity every day of the week — it is called family worship."
"Both through the preaching of the word and informal shepherding of the congregation, the church leadership aspires to equip our dozens and dozens of youth pastors to successfully minister to the diverse needs of the many individuals and special interest groups within their respective organizations. Because we don’t want to leave anybody behind, we have instructed these church organizations to reach out to the young, the old, and the infirm — the singles, the divorced, or abandoned — everybody, such that we will have a comprehensive outreach for every special interest group represented by the membership of our assembly of believers. As a result, these organizations sponsor events that include hospitality and evangelism outreach, one-room schoolhouses (usually meeting in the family den), foreign missions (to Mexico), and literally hundreds of other activities designed to meet the needs of the organizational members."
Douglas W. Phillips, Our Church Youth Group
It's called "family integrated church." or just Church.