Technically, anything that a ministry does for the family could be called family ministry but that's actually part of the problem. There is a difference between doing something FOR the family and doing something WITH the family. Family ministry should not be another program you add to your list of programs. It should develop the process that drives how both the church and the home combine their effort to influence the next generation in their faith and character. If you really believe that nothing is more important than someone's relationship with God, it makes sense to combine the influences of the home and church.
