Divorcing an illegal alien uses the same process as divorcing a US citizen. You must file a petition for divorce and get him served.
There is a presumption that all property acquired during the marriage is community property. If he claims that the house is his separate property, he must prove that by clear and convincing evidence, which may be very hard to do. Assuming that he is unable to prove that the house is his separate property, the court can award the house to you, to him or have it sold and split the proceeds.
The fact that your husband has a fictitious social security number does not affect any of this. The point is, he bought the house during the course of the marriage and it is presumed to the community property. You can ask the court to award it to you. Just remember, asking and getting are two different things.
The Court is charged with the responsibility of making a "just and right, fair and equitable division of the community estate." What you consider "just and right, fair and equitable" may be quite different from how the Court sees it.
