Dear PJ:
I must apologize for not being precise. You are looking for a very precise answer. I always debate how technically precise I should be especially on canonical issues. I tried to give accurate answers but do not wish to confuse people. Many canonical issues, and some of the nuances of Church teaching, can be very technical, complicated, and confusing.
You are wanting, however, a precise and technical answer. To do that let me quote from a commentary on Canon law 1056:
To say that marriage is indissoluble means that it is a perpetual relationship which not only should not be terminated but cannot be terminated, even if the couples existential relationship is irretrievably broken. Canonical tradition distinguishes between the intrinsic and extrinsic indissolubility of marriage. All marriages, whether the spouses are baptized are not, are intrinsically indissoluble. That is, once the marriages validly entered, it cannot be dissolved by the subsequent withdrawal of consent of the parties. A marriage is extrinsically indissoluble way cannot be resolved either by the intervention at external authorities or by the realization of certain conditions. While the church does not recognize the power of civil authorities to dissolve marriages, it does claim the authority, under certain conditions, to dissolve the non-sacramental marriages involving at least one unbaptized person and sacramental marriages that have not been consummated. Thus, current church law considers only sacramental marriages that have been consummated the extrinsically indissoluble by any cause except death.
Thus, you are correct in saying that the Church affirms that natural marriages are by nature indissoluble. Natural marriage, however, is instituted by man. Sacramental marriage, on the other hand, is instituted by God. As God tells us, "what therefore God has joined together, let no man put asunder." Thus, no authority, whether civil or ecclesiastical, can dissolve what God has established in Sacramental marriage. The State may presume it has the power to dissolve marriages, but the Church does not recognize civil authority in this matter. Civil laws on marriage merely establish legal rights and obligations, but it is God who establishes a genuine marriage.
While natural marriages are inherently indissoluble intrinsically, they may be dissolved extrinsically by the proper authority. The Church considers only "sacramental marriages that have been consummated to be extrinsically indissoluble".
For the Christian, that is for one who has been validly baptized, Sacramental marriage ought to be the goal. For a Catholic, the Church requires marriage only to another baptized Catholic. For pastoral reasons Bishop may give permission for a Catholic to marry a non--Catholic baptized Christian. Since the non-Catholic spouse is validly baptized, this marriage is Sacramental.
For a Catholic who wants to marry a non-Christian, special dispensation from the Bishop is required. While such a marriage can be blessed in the Church when the Bishop has given a dispensation, the marriage is not Sacramental.
The Sacrament of the Marriage provides a "special firmness", or extra bond from God beyond that provided from natural law. As the Catechism states:
1638 "From a valid marriage arises a bond between the spouses which by its very nature is perpetual and exclusive; furthermore, in a Christian marriage the spouses are strengthened and, as it were, consecrated for the duties and the dignity of their state by a special sacrament."
For Christians, and for the Catholic Church in particular, a valid marriage must be valid according to natural law and Church law. It is only when both natural law and Church law are satisfied that the marriage becomes Sacramental.
Natural marriages are intrinsically indissoluble but extrinsically dissoluble by the proper authority under certain conditions. Sacramental marriages are are both intrinsically and extrinsically indissoluble.
I think I am describing this correctly, but I am not a canon lawyer. If there are any canon lawyers out there who are reading this and wish to correct or further explain this question, please do so.
God Bless,
Bro. Ignatius Mary