"the question is if the mortage is not in both of their names". Confusing but I assume you meant the title to the house is not in both of your and your husband's names but is entirely in his name. Then, it's probably his separate property and the surviving spouse's share when there is no will is 1/3 since he will leave behind more than one child.

However, it's possible that the house is community property (CP) if it was purchased during your marriage, the downpayment was from your husband's wages (which are CP) and you both have been making payments from wages. If the house is CP, your share as a surviving spouse is all of it. You should check with a family lawyer or probate lawyer to make sure if the house is CP or only a portion of it by now.

https://www.lawguru.com/cgi/bbs/attyPages/liem.html

Note: The above response is provided for legal information only and should not be construed as legal advice, nor to create an attorney-client relationship, which can only be established through payment of consideration. We do not offer free advice except for the information provided herein on LawGuru which has been screened. If follow-up advice on your specific situation is desired, we offer a paid consultation in person if you are in the Los Angeles area, or by phone or email.

I echo what Mr. Doan said and add: if he has mental capability you should have him get a will done ASAP. Handwrittten wills are often effective (in his writing, signed and dated). If it's too late then you will need to do some sort of probate procedure after death. A spousal property petition may work depending on the facts. I encourage you to hire an experienced probate attorney in your area. I am a certified specialist in probate, estate and trust law. -John