Can an unmarried couple baptize their baby if one parent was not bapitzed in the Catholic church?

Presuming that the child will be brought up in the Catholic faith and that the custodial parent does not have an objection to the baptism, an unmarried couple, where one party is not Catholic, may ask to have their child baptized in the Church. The pastor will have to decide whether the unmarried status of the parents is an issue (usually due to scandal) which may call for delaying baptism, but for the good of the salvation of the innocent child, baptism is never outright denied. Normally such baptisms should not take place publicly (for instance, at Sunday Mass,) which would call attention to the shameful circumstances existing in a family living without the benefit of marriage. Unmarried parents should be prepared to discuss with the priest whether they wish to 'normalize' their relationship in the Sacrament of Marriage. Indeed, if the parents still lack maturity or freedom to enter into the sacrament, it may be best NOT to advise, recommend, or even allow marriage. Oftentimes, parents have no intention of entering into marriage-- certainly in this case, the parents should not be living a conjugal life which may beget more children into this unfortunate situation. A situation where parents persist in living outside of the Sacrament of Marriage may cast doubts on whether a child is being raised in the faith, as these parents have placed themselves outside of the grace of the Church. In such a case, a pastor may elect to 'delay' a baptism until such time that proper Catholic formation is assured. This is a touchy pastoral situation which can only be resolved by a local pastor who knows the particular situation. In the Rite of Baptism, parents will be asked to affirm their resolution to bring their child up in the practice of the faith. Parents who are baptized Christians (Catholic or not) are asked to renew their own baptismal vows. In the case that one parent is not baptized (for instance, if one is Jewish or Muslim), they do not in the integrity of their conscience profess faith in Jesus Christ as God, and should properly decline to participate in this element of the rite. (Of course, if they are able to make such a profession, these non-Christian parents can and should become Catholic, but that's a whole different question...)