Since the Bible doesn't expressly address this question of an unbelieving spouse, nor call the person "holy" the way it does the child of a believer; and with the possibility (and historic fact) that human society goes through shifts over time--the question of how to deal with an unbelieving spouse within the external administration of the covenant of grace is no where near as plain as the case of the child.
In the chosen translation above, it is not clear to the reader that there is a verb-form meaning "to sanctify" in the case of the spousal relation; and an adjective in the predicate state as the final description of the child. The child is "holy," it is a quality that belongs to it; whereas in regard to the spouse, the sanctity mentioned is purely a product of the existing marital relationship.
For example, some of the replies in the thread seem to take for granted that the wife is the unbelieving spouse, without actually spelling that assumption out. An argument might be put forward that as head of house, a Christian husband might lead his willing wife into the church, into the visible administration. But this argument would have a difficult time, if the "unbelieving spouse" was not head-of-house, i.e. the husband (in any biblically ordered house).
This disparity shows perfectly the lack of symmetry to the proposition, if trying to force Paul's expressions regarding covenant children into a supposed logical entailment concerning spouses.
Let me suggest, that in a particular situation (overseen by competent elders who are thinking this matter through for themselves), with a compliant wife eager to follow her husband's lead, who desires (as much as anyone can know her own heart) to identify with the Christian faith, willing to set herself in subjection to the covenant's external administration, baptism would be in order. I hardly know how it should be avoided, if she is clearly willing to take on the faith albeit she is ready to learn it as a child, alongside her own children.
I must think, though: why not take the time to lead her through a new member's class, and ask her if she afterward confesses as her faith the doctrine of this church (in rudimentary form) and is hopeful in time and attendance on the means of grace to increase her knowledge? Even if she continues in so shallow a state of faith that she is not ready to come to the Lord's Table for a while, baptism at least seems warranted.
On the other hand, it does not seem to comport with any biblical description I know, to have a believing wife lead her faithless husband (and putative head of house) to church and straight to the baptismal font. This does not follow. Nor are we deciding what might be done in every curious situation someone can dream up. We aren't baptizing children-of-believers based on logical entailment, but on the clear commandment of Scripture (to the Presbyterian, it is clear as day; the command is in Gen.17, the new covenant application is found at least but not limited to the echo of Abrahamic promise in Act.2:39).
What makes up a household can and has varied over time and place. Justification offered for unlimited inclusion in the concept is as erroneous as artificial limitations. What has never changed is the order of creation, and the clear biblical designation of the husband/father as head of house, as long as he lives. Even sinful abdication of that role (in its entirety; not every house needs the same set of protocols as to how this fact is worked out) doesn't remove the duty, for which God will call a husband/father to account. So then, we should consider for our own moment in time which of all the people who happen to live under one roof, or within certain walls, are proper candidates for baptism, given the Bible's criteria (which obviously includes household baptism).
For these reasons, there is no symmetry in Paul's statement, 1Cor.7:14; the inference that the unbelieving spouse necessarily has a right to admission (outwardly) to the covenant of grace is false. There may be reason to admit, or there may not be. But why assume the hardest case, when willingness to BE, to begin and continue a Christian is a more likely situation? Otherwise, the unbeliever (husband or wife) will just stay away and refuse baptism.
