Dear Magali:

The teaching on marriage involves several levels.

On teaching that is De fide (of the faith), that is, infallible dogma officially declared by the extraordinary Magisterium (e.g. ex cathedra), to which if one doubts or refutes this teaching is a heretic. This is Level 1 teaching and includes the following:

• Marriage is a true and proper Sacrament instituted by God
• From the sacramental contract of marriage emerges the Bond of Marriage, which binds both marriage partners to a lifelong indivisible community of life
• The Sacrament of Marriage bestows Sanctifying Grace on the contracting parties

On teaching that is Sententia certa (certain faith), that is, definitive teaching that has always been taught by the ordinary Magisterium. Pope John Paul II added a paragraph in Canon Law to definitive declare that this level of teaching (Level 2), is indeed infallible, but does not quite rise to the level of heresy. On this level we have several teachings:

• Marriage was not instituted by man, but by God
• The primary purpose of Marriage is the generation and bringing-up of offspring. The second purpose is mutual help and the morally regulated satisfaction of the sex urge.
• The essential properties of Marriage are unity (monogamy) and indissolubility
• Every valid contract of Marriage between Christians is of itself a sacrament [my note: to be a Christian one must be validly baptized]
• The contracting parties in Matrimony minister the Sacrament each to the other
• The Church possesses the sole and exclusive right to make laws and administer justice in the matrimonial affairs of baptized persons, in so far as these affect the Sacrament

These teaching compose Level 1 and Level 2 doctrine. They are infallible and not not up for discussion. They cannot be changed by anyone, including popes and councils.

As the item mentions, the Church possesses the " sole and exclusive right to make laws and administer justice in the matrimonial affairs of baptized persons." Concerning this aspect, the Church has promulgated many canonical regulations that must be followed for valid and licit marriage.

For example, although non-Catholic Christians who are validly baptized contract a Sacramental marriage by virtue of their baptism, if one of the spouses is Catholic, or if both are Catholic, the Church requires what is called "canonical form". This means that anytime a Catholic gets married the wedding must be Catholic, that is, it is to be conducted in an appropriate place, usually a Catholic Church unless a dispensation is granted (CIC 1127 §2, and the consent and vows must be offered before a Catholic Priest or Deacon. One cannot have a Catholic wedding and then a wedding in the denomination of one's spouse. It must be Catholic only, although the pastor of a spouse's denomination may be present and offer a blessing. But, only the priest or deacon can receive the consent and vows. (CIC 1127 §3)

For a Catholic to marry a baptized non-Catholic Christian (called a mixed marriage), the Catholic person must receive permission from the bishop if there is "just and reasonable cause" (CIC 1125). To receive this permission the Catholic spouse must promise that nothing will hinder them from practicing the faith, and that the kids must be raised Catholic.

For a Catholic to marry a non-Christian (someone not validly baptized) is called a Disparity of Worship (CIC 1086). A Catholic who marries a non-Christian has an invalid marriage, unless the bishop grants a dispensation. A dispensation is the suspension of this impediment. The Church has the authority to grant such dispensation, through its bishops, by virtue of the infallible doctrine:  The Church possesses the sole and exclusive right to make laws and administer justice in the matrimonial affairs of baptized persons, in so far as these affect the Sacrament. This dispensation is to be granted only when there is some "just and reasonable cause". The conditions of CIC 1125 and 1127 still apply.

In the case of a marriage recognized by the Church of baptized person and a non-baptized person, such marriage is not sacramental, but when all canonical requirements are met, such as episcopal dispensation, canonical form, etc., there is no sin in the marital embrace of such married persons (even though the marriage is not Sacramental). 

A valid Sacramental marriage cannot be dissolve except by death. An Decree of Nullity is a declaration from the Church that a Sacramental marriage never existed, and thus there is nothing to dissolve. In such cases, any children are NOT bastard. Children are illegitimate by civil law on Marriage, and are considered by the Church to always be blessings. Thus, a decree of nullity of a marriage has no effect on the children of that couple.

If a couple has a invalid marriage, and are willing to take the steps to regularize their marriage (e.g. get needed annulments, remove other impediments, then a blessing by the Church, etc.), that is possible by Convalidation (CIC 1156-1165)

Canon Law concerning marriage, begin with Title VII, CIC 1055. Mixed Marriage are regulated in Chapter VI of Title VII, and disparity of cult is in Chapter III of Title VII. The factors that are involved in annulments are too complicated to discuss on this forum, but one can look it up begining with Canon Law Chapter IX (cc. 1141-1155) - Article 1 is on the first screen and Article 2 on the second screen. Convalidation of Marriage is discussed in Chapter X (cc. 1156-1165), with Articles 1 and 2 on separate pages.

God Bless,
Bro. Ignatius Mary