A married woman in California has the right to buy her own home. However, any assets accumulated during the marriage are classified as marital assets because California is a community property state. Your husband will automatically have ownership rights to the home even if he isn't listed on the mortgage, but he can choose to give up his share of ownership.
In equitable distribution states, only the borrowers listed on the mortgage are responsible for making the mortgage payment. If a spouse defaults, the lender can't hold the other spouse liable. Since California is a community property state, the laws are different. All assets and debts that were acquired during the marriage are marital property, regardless of who "owns" the home. Although you're signing the contract, the lender can go after your husband if you default on the mortgage.
Your husband will have equal ownership rights to the home. If you divorce, the home is viewed as a marital asset subject to equal division. If your husband agrees, he can sign over his share of interest to you by completing an inter-spousal transfer deed. This can be done at the closing or anytime after you purchase the home. An inter-spousal deed is reserved exclusively for transfers between spouses and is exempt from county transfer taxes.
Your Credit and Income
Although you're married, you can legally apply for a mortgage solely in your name. The ability to qualify is based on your credit score and income if you exclude your husband from the application. If you have joint bank accounts or other investment accounts in both names, the lender can take those into consideration when calculating your assets.
Your Spouse's Debt
Your husband's income can't be used to help you qualify for the mortgage if you leave him off the application, but his debts may still count if you're applying for an FHA or VA loan. Since all assets and debts are considered jointly owned, his debts are your debts. Lenders can factor his debt into your debt-to-income ratio, resulting in more debt and less income.