A - Thanks for the question. Yes, a non-Christian and a Catholic can be validly married, but the marriage will not be Sacramental. Marriage is not only for Christians, but for all people. Thus, marriage can be validly entered into. But, for it to be a Sacrament, both spouses must be Christian (i.e. validly baptized). This is because the spouses confer the Sacrament upon one another and to be disposed to receive any other Sacrament, you must be baptized first. Thus, the Church believes that any valid marriage between any two Christians is a Sacramental marriage in addition to being valid.
For a Catholic to marry a non-Catholic, they must first get permission from the Bishop. There are two different kinds of permission needed. If you are marrying a non-Catholic Christian, then you need "permission to enter into a mixed marriage." If the person is a non-Christian, then you need "dispensation from disparity of cult."
As for an atheist, the same rules apply. Just because they lack belief, the Church doesn't see them any differently than any other non-Christian.
From the US Bishops:
A valid Catholic marriage results from four elements:If an atheist and a Catholic both are able to have these conditions met, then they can marry validly in a Catholic Church - though the marriage won't be Sacramental.
Exceptions to the last requirement must be approved by church authority.
- the spouses are free to marry;
- they freely exchange their consent;
- in consenting to marry, they have the intention to marry for life, to be faithful to one another and be open to children; and
- their consent is given in the presence of two witnesses and before a properly authorized Church minister.
I hope this helps.