One thing I think it's important to realize when it comes to understanding the role that men play in their families -- and I can say this speaking both personally and professionally -- is that religion tends to domesticate men. It makes men more likely to focus on the needs of their wives and their children. We know that more religious fathers are more involved and more affectionate with their kids and, in fact, religion seems to matter more for fathers than it does for mothers, because most moms are very involved with their kids. There is more heterogeneity when it comes to dads. Some dads are really involved and some dads are not so involved, and because there is more difference in the levels of paternal involvement, any factor that makes them family-focused will have an impact.
What I find in my work is that religion is more predictive of greater involvement for dads than it is for moms. Religion is one of the few institutions that men encounter in their daily lives that really encourage them to think about their families. At work, in the bar, at Yankee Stadium, men for the most part are not encouraged to think about their families. Whereas if they go to a synagogue on Saturday or to a church on Sunday, they will often hear a message about the importance of loving their kids, the importance of setting aside time for their children. These are reasons why religion is important, particularly for dads, in making them more engaged as parents.