Before we get to scholarly opinion, you're married to someone who is a Muslim and believes themself to be a woman. There's Islam-related consequences to this, e.g.
- they may view your marriage as a lesbian marriage;
- they may not believe the rights and responsibilities of being a husband apply to them.
To stay together, you're going to have to navigate these Islam-related consequences, along with the non-Islam related consequences.
What we know:
Allah determines who's male and who's female while the child is in the womb:
And then, if Allah wishes to complete the child's creation, the angel will say. 'O Lord! A male or a female? O Lord! wretched or blessed (in religion)? What will his livelihood be? What will his age be?' -- Sahih al-Bukhari 3333 (sunnah.com)
There's numerous gender-related birth defects seen in mankind.
Islam does not recognize same-sex marriage. Moreover, same-sex sexual activity is illegal and punishable in various Muslim-majority countries. See LGBT in Islam, Wikipedia.
What do scholars say:
There's two opposite ways scholars think about this, and the Islamic validity of your marriage will vary according to the scholar. So, it'd be best to be careful with who you ask about this.
1. A person's gender is equivalent to their anatomy at birth.
People are ordinarily born with well-defined genitals (intersex people are the exception). Some scholars believe this determines one's gender. Here's one example:
The transition of this category is a great crime: it is mutilation, changing the creation of Allah and imitation of the opposite sex—and those who do these things have been cursed by the Prophet (saws). ... having sex reassignment therapy is a prohibited act according to Shari`ah ... -- AMJA Fatwa Committee, 2008 (Fatwa 21701)
2. A person's gender is determined by Allah, and may differ from their anatomy at birth.
Or equivalently: There's a small proportion of exceptions to Opinion 1.
While Allah does not make mistakes, biology can result in a wide range of imperfections and defects. These can be corrected using modern medicine to a certain extent. Here's one example:
That being so, the rulings derived from these and other noble hadiths on treatment grant permission to perform an operation changing a man into a woman, or vice versa, as long as a reliable doctor concludes that there are innate causes in the body itself, indicating a buried [matmura] female nature, or a covered [maghmura] male nature, because the operation will disclose these buried or covered organs, thereby curing a corporal disease which cannot be removed, except by this operation.
Indeed, it is obligatory to do so on the grounds that it must be considered a treatment, when a trustworthy doctor advises it. It is, however, not permissible to do it at the mere wish to change sex from woman to man, or vice versa. -- Egypt's former grand Mufti Al-Azhar Sheikh Mohamed Tantawi (1988)
I'm not in a position to make judgement calls on particular marriages, particularly on a topic so intricate, so I'll leave that part out.