Canon 1127. §1 The prescripts of can. 1108 are to be observed for the form to be employed in a mixed marriage; if however a Catholic party contracts marriage with a non-Catholic party of an Eastern Rite, the canonical form of the celebration must be observed for liceity only; for validity, however, the presence of a priest is required notwithstanding whatever else is to be observed in accordance with the law.
[revised wording according to m.p. De concordia inter Codices, 31.V.2016]

§2 If there are grave difficulties in the way of observing the canonical form, the local
Ordinary of the catholic party has the right to dispense from it in individual cases, having however consulted the Ordinary of the place of the celebration of the marriage; for validity, however, some public form of celebration is required. It is for the Episcopal Conference to establish norms whereby this dispensation may be granted in a uniform manner.

§3 It is forbidden to have, either before or after the canonical celebration in accordance with §1, another religious celebration of the same marriage for the purpose of giving or renewing matrimonial consent. Likewise, there is not to be a religious celebration in which the catholic assistant and a non-catholic minister, each performing his own rite, ask for the consent of the parties.

§1. Ad formam quod attinet in matrimonio mixto adhibendam, serventur praescripta can. 1108; si tamen pars catholica matrimonium contrahit cum parte non catholica ritus orientalis, forma canonica celebrationis servanda est ad liceitatem tantum; ad validitatem autem requiritur interventus ministri sacri, servatis aliis de iure servandis.

§2. Si graves difficultates formae canonicae servandae obstent, Ordinario loci partis catholicae ius est ab eadem in singulis casibus dispensandi, consulto tamen Ordinario loci in quo matrimonium celebratur, et salva ad validitatem aliqua publica forma celebrationis; Episcoporum conferentiae est normas statuere, quibus praedicta dispensatio concordi ratione concedatur.

§3. Vetatur ne, ante vel post canonicam celebrationem ad normam §1, alia habeatur eiusdem matrimonii celebratio religiosa ad matrimonialem consensum praestandum vel renovandum; item ne fiat celebratio religiosa, in qua assistens catholicus et minister non catholicus insimul, suum quisque ritum peragens, partium consensum exquirant.