TL;DR: Islam forbids eating pork, etc., and this applies to every human (although a non-Muslim wouldn't ordinarily follow Islamic sharia). Fatawa encourage a Muslim husband to encourage or instruct his non-Muslim wife to not eat pork. For Christianity in particular, they highlight how pork is described as unclean in the Bible. A husband is forbidden from "cooperating in sin" (so he shouldn't encourage eating pork), but it seems unlikely that merely refraining from forbidding his wife from eating pork is sinful.
There are certain things which are forbidden in Islam to be consumed (e.g., pork, alcohol, animal blood). In principle, these things are forbidden whether or not you're a Muslim: the Qur'an and Sunnah don't list exceptions.
This means that things that are forbidden to Muslims are also forbidden to them, such as drinking alcohol, eating pork, introducing innovations or celebrating them.
However, someone who is not a Muslim wouldn't necessarily adhere to Islamic sharia. For comparison, cows are considered sacred in Hinduism, while Muslims consider eating beef as permissible. In this case, Hindu beliefs do not affect the Muslim diet.
An About Islam article encourages a husband to appeal to his Christian wife not to eat pork, highlighting how it's also mentioned as unclean in the Bible (see Ruling on eating pork in Christianity as per Bible?). For this reason, an About Islam fatwa writes:
As for eating pork, it is even prohibited in all religions, and as such the husband can prevent her from eating it.
(Here "all religions" presumably means Christianity, Judaism, and Islam.)
Indeed, the aforementioned Islam Q&A fatwa uses Qur'an 6:66 (...protect yourselves and your families from a Fire whose fuel is people and stones...) as justification that a Muslim men "should stop his wife from committing any of these actions", including eating pork.
Also note that Christianity espouses a wife's obedience to her husband (...wives should submit to their husbands in everything... Ephesians 5:22-34). However, it's unclear how much this applies when a Muslim husband forbids his wife to eat pork, given that the Bible discourages (or perhaps forbids) marriage to non-Christians in the first place: Do not be yoked together with unbelievers (2 Corinthians 6:14); see also Christianity.SE.
It seems unlikely that a husband merely not disallowing his wife to eat pork would count as a sin for him. While the Qur'an encourages ...forbidding what is wrong... (Qur'an 3:104), it should be weighed against ..no bearer of burdens will bear the burden of another... (Qur'an 35:18) and For you is your religion, and for me is my religion (Qur'an 109:6).
Actively encouraging or facilitating eating pork would be regarded as sin:
... do not cooperate in sin and aggression ...
... they may bear their own burdens in full on the Day of Resurrection and some of the burdens of those whom they misguide without knowledge ...