Believe it or not, this was one a controversial question. Today, many “mixed marriages” take place every year, joining together people of different faiths into one. While it may seem commonplace and routine today, this is only because of major shifts in the Church’s approach to ecumenism, leading to a reform of the liturgy.
If you’re preparing for your own wedding today, the USCCB has some great resources for you to use.
In the case of marriage between a Catholic and a non Christian, I don’t see why the Church should have any role in the marriage. The non Christian rejects the authority of the Church on any religious issue. Why should the Church have any interest in a marriage with such a person