We propose a model that generates a family network based on real-world family network data. We use this model to study the extent to which distances to union and the number of children characterize family networks. To determine how accurate our model is we use persistent homology to identify and compare the structure of our modeled family networks to real-world family networks. To accomplish this, we introduce the notion of a network's persistence curve, which encodes the network's set of persistence intervals. Using the bottleneck distance allows us to measure the difference in the homological structure between any pair of networks. We also study how the distribution of distance to union and the distribution of children build family networks. What we find is that these two features of distance to union and number of children allow us to fairly accurately recreate family networks at least at the level of their persistent homology.