What church?
Can anyone say with certainty what denomination church conducted the ceremony? It seemed dangerously near Catholic, but I can't believe for a second that filmmakers in 1950 would have depicted the upper middle class "Banks" family as being Catholic.
Given the pastor's vestments, the kneeling, and all the "Father, Son and Holy Ghost"-ing, I'm guessing it's as close to the C of E as they have in the US -- namely Episcopalian?