A marriage is between two people. Families don't go to the courthouse together to get marriage licenses and only the wedding couple is named on the marriage license.
After that, depending on tradition and the cultural norms within your extended family, the blending of two families may or may not happen.
We live down the block from our son's girlfriend's parents. In 10 years, we have met them a couple of times. When they get married, we will remain cordial but there will never be a blending of families due to extreme differences in beliefs. My son rarely goes over there himself because they do not approve of him as he is not part of their religion. The only reason they have not married yet is that they will not give their approval (they have been joined at the hip for 10 years now, all through high school, college and now grad school.) They have decided to wait a bit longer until they are more established before she alienates her parents and gets married.