Once again, this is more complicated than the question seems. First let us understand what marriage is. Marriage is a practice common to all cultures in all ages. It is, therefore, a natural institution, something common to all mankind. At its most basic level, marriage is a union between a man and a woman for the purpose of procreation and mutual support, or love. Each spouse in a marriage gives up some rights over his or her life in exchange for rights over the life of the other spouse.
Now to the question submitted: The "straight answer" is simply "yes," but let’s understand also the "why."
In the Sacrament of Marriage, a baptized Christian man exchanges vows with a baptized Christian woman. Before Almighty God, they promise to each other a love that is faithful, permanent, exclusive, self-sacrificing and life-giving. Through marriage, a couple now enters into a new public state of life both in the eyes of the Church and society; therefore, the celebration of the marriage rightfully ought to be public with the vows exchanged before a priest, and the faithful gathered for the ceremony. (Cf. Catechism, No. 1663.) Given this basis, a Catholic (either baptized as a Catholic or later entering the Catholic Church after having already been baptized in another Christian denomination) is bound to be married in the Catholic Church. The Church in which one has been baptized and confirmed, receives Holy Communion and professes faith, ought to be the Church in which one is married. Consequently, whether a Catholic is marrying a Catholic or a baptized nonCatholic Christian, the normal expectation is for the marriage to take place in the Catholic Church and for the children to be raised in the Catholic faith.
However, when a Catholic is marrying a non-Catholic but baptized Christian, legitimate circumstances may arise where the couple would like to be married in the Church of the non-Catholic. Such special circumstances include recognizing a special or long-standing relationship with a minister, or preventing family alienation. In such a case, the couple would complete the regular Catholic marriage preparation, and with the permission of the Archbishop, can then be married in a different situation. The Catholic party would also attest to his intention of not leaving the Catholic Church and of promising to baptize and raise the children in the Catholic faith. The nonCatholic party would be informed of these promises, attest to understanding these promises and in turn promise not to interfere in their fulfillment. The Church requires a dispensation because the Archbishop, as shepherd of the archdiocese and guardian of the souls, must insure that the couple is prepared as best as possible for marriage and is ready to enter into Holy Matrimony. With such permission, the wedding is valid in the eyes of the Catholic Church. (Cf. Code of Canon Law, No. 1124-25).
If a Catholic enters marriage outside of the Catholic Church without the necessary dispensation, then the marriage is considered invalid and is not recognized by the Church. I am surprised by how many people are unaware of this obligation. Too often, couples register in the parish indicating that they were not married in the Church. It never ceases to amaze me how some never realized they had to be married in the Catholic Church or first receive the proper dispensation to be married elsewhere. Sadly, some of these people then resent the fact that the Church considers their marriages invalid and that they will have to follow the proper steps to have them validated. Clearly, pastors, parents and religious educators need to stress the importance of marriage in the Church to those entrusted to their care.