If my husband is being sued for a debt can they come after our house if it’s only under my name?

CA is a community property state.  And in such a state most debts incurred by either spouse during the marriage for the benefit of the community are owed by the "community" i.e. (the couple). This is true even if only 1 spouse signed the paperwork for a debt.  However, if a spouse incurrs a debt prior to marriage it won't automatically become a joint debt, it typcially remains separate debt. You did not indicate just when your husband bought the car. 

If the judgement is solely in your husband's name the creditor would have to go to court and sue you in order to obtain a judgment in your name. Again, depending on just when this debt was incurred (prior/after marriage) they may or may not be able to do this.

Even if they do not obtain a judgment against you, they may be able to go against half of the house since it may be considered to be a community asset if you purchased it after your marriage. Accordingly, the responsible spouse's half (your husband's share) of the community property may be used to repay debt.

As a practical matter, they wouldn't force the sale of the house but they could put a lien against it. Additionally, in CA you can obtain protection for some of the equity you have in your home by declaring it a "homestead".  Without a homestead declaration the creditor is entitled to any equity up to the amount of the lien; with a homestead declaration a portion of the equity is exempt from collection via the lien.  However in order to claim a homestead you must meet certain requirements. To find out more you should speak with directly with an attorney in your area.

If your husband is sued for a past debt and the creditor gets a judgement against him then they can execute on the judgement in any way permitted under the law.  That means that they can levy on property that is his.  The can not levy on property that has your name on it because the judgment does not have your name on it.  This is not to say that you will not be effected.  On the contrary, if they garnish his wages that will effect you; if they levy a joint bank account that will effect you; if they take your tax refund that will effect you.  It may be a good idea to make a deal and settle the matter.  Good luck.