Welcome to Islam, you will soon witness the beauty of the religion, the peace and tranquility it brings to you and please don't be disappointed by the indiscipline among majority of its followers, we're trying, make supplication for us.
Known (Sunni) Shari'a Point of View
I will try to explain the shari'a point of view (links are included in the text but may also refer to other parts) According to the following Verse of Quran:
O you who have believed, when the believing women come to you as
emigrants, examine them. Allah is most knowing as to their faith. And
if you know them to be believers, then do not return them to the
disbelievers; they are not lawful [wives] for them, nor are they
lawful [husbands] for them. But give the disbelievers what they have
spent. And there is no blame upon you if you marry them when you have
given them their due compensation. And hold not to marriage bonds with
disbelieving women, but ask for what you have spent and let them ask
for what they have spent. That is the judgement of Allah ; He judges
between you. And Allah is Knowing and Wise.
A woman who converted to islam shouldn't stay (return to her) with a non-muslim Husband. This means she should reject having intercourse with him and they should be divorced after the waiting period. This is the clear Sunni point of view as we find in the Quran a Verse which explains this duration:
O Prophet, when you [Muslims] divorce women, divorce them for [the
commencement of] their waiting period and keep count of the waiting
period, and fear Allah , your Lord. Do not turn them out of their
[husbands'] houses, nor should they [themselves] leave [during that
period] unless they are committing a clear immorality. And those are
the limits [set by] Allah . And whoever transgresses the limits of
Allah has certainly wronged himself. You know not; perhaps Allah will
bring about after that a [different] matter.
Now during this time you could try to convince your husband to convert to islam with all you can. As the scholars also, say if one of married couple convert to islam and the waiting period passed and the other also became muslim that their former husband/wife is the best to keep, this means their marriage is still acknowledged and they can live together as before as husband and wife. therefore in an islamic country a Judge would either divorce you after the waiting period or confirm your marriage. During the time of the waiting period no muslim man can marry you even if islam is regarding your conversion as a reason for divorce. But afterwards (legally from a shri'a point of view but you must have been divorced) it is possible.
In a long Hadith in Sahih al-Bukhari you also find that O'mar ibn al Khatab divorced two of his non-muslim wifes after the revealing of the Verse (60:10).
So far this are the known shari'a point of views which end that a woman would be separated/divorced after her waiting period (3 months) if she converts and her husband didn't. But one must take into account that these rules where made for converts who converted in dar al-islam which nowadays means they converted in a muslim country!
Here are some related Fatwas in Arabic as an Addition:
Dar al-ifta' al-Massriya
Situation for converts in non-muslim countries
For a converted woman who lives in a non muslim country one should take into account her situation and maybe look at some not that popular fatwas about the matter we can find that Sheikh al-Qaradawy quotes that ibn al-Qayyim al-Jawziya counted 9 different opinions here just 3 of them revealed in the article:
- We can find that 'Omar ibn al Khatab (May Allah be pleased with him) as quoted by ibn al-Qayyim that he gave a former christian woman, which converted but didn't leave her non muslim husband (and homeland?) the choice between leaving her husband or staying beside him, Sheikh al-Qaradawy interprets the narration as even they will stay together as husband in wife with all meanings of the matter (including intercourse!).
- An other Narration mentioned by ibn al-Qayyim from 'Ali ibn Abi Talib (May Allah be pleased with him) said that she could stay with him and wait for him to convert but she shouldn't let him make possession of her (having intercourse) this was the favorite opinion of ibn al-Qayyim and ibn Tayymiya.
- A 3rd Narration quoted by ibn al-Qayyim from Imam az-Zuhari (May Allah be pleased with him) says that they could stay toghether until a court ( i guess he this means: an islamic court) or a higher authority separates them!
These 3 Opinions are valid as in (60:10) the converted woman left their non-Muslim husbands in Mekka Mekka (ard-al-Kufr) and came to Medina (ard al-Islam) to a Muslim community/country! So if (only) the wife converts and leaves her husband to a Muslim country the situation will change and the former fatwas should be applied!
A point which is stated by Abu al 'ala' al Mawdodi is: That if the Marriage itself is regarded as invalid in islam they would be divorced automatically: For example a woman who married a mahram.
Abu al 'ala' al Mawdodi added that in any case the woman should reject having intercourse with her (non-muslim) Husband and after the waiting period she could choose still to wait for him or to leave him. As from a shri'a point of view her marriage is still valid but considered as made temporary inactive! And he -in case she wants to separate- advises to do a legal divorce!
These statements are based on an article which reports some discussion in the European Council For Fatwa and Research.
Additions and Conclusion
I know from a shi'i friend that his sister married a christian (all living in Germany) with a kind of contract. But i don't know the details and the situation here is different and the story seems to be a special case which might not be accepted by scholars as one may conclude from the answers of shi'a brothers on What's the stand of Islam on a Muslim woman marrying a non-believer??
According the Sunni point of view nikah al-Muta' is haram because it has a touch of zina and it is considered as abrogated!
Therefore i can only suggest to make your effort to convince your husband to become a Muslim and hope you will succeed.
And Allah knows best!