If you lived in the home for a substantial time during the marriage, than it will probably be ruled to be a marital asset and divided in the divorce, either by selling it and dividing the profits or by giving it to one of you. Regardless, since there was domestic violence, it would be a good idea if you found a friend or family member to live with pending the resolution of the divorce.
If you want a lawyer to help you, I would suggest speaking with Bay Area Legal Services (bals.org) which is a legal aid provider in the area.
My response to this question does not mean I agree to represent you in any proceedings. This information is also not subject to attorney-client privilege.
I believe it will really depend on the specific facts of your case. If the property was deeded to him but was paid for with marital monies then there's a good chance it's a marital asset. If it was deeded to him but the value was enhanced by the expenditure of marital monies or marital labor, then even if it's non-marital property the increase in value due to those efforts and expenditures is a marital asset.
If you live there with him, it's unlikely he can throw you out without some sort of court order.
You mentioned that there had been domestic violence. If you are the victim of domestic vilence and are in fear for your safety you should definitely contact law enforcement and consider filing a Petition for Protection from Domestic Violence. The Court in such a case has the authority and discretion to grant sole use and possession of the home to you regardless of the way it is titled.