If my husband and I bought?

if he leaves his half to her she owns it once he dies and you two must deced what to do from there.

No, he can't give his half of the house to her. When he dies, it will go to you. If when you die, you want to leave it to her, you can but you don't have to. Simple as that.

[edit] - Here's more:

Joint ownership is most often applied in the real estate market, where it refers to two people who jointly own a home. In most cases, these two people are a married couple. This type of joint ownership can reduce hassle. It is not necessary for a person to wait for probate in order to own the whole house if his or her spouse dies.

When a spouse dies, it may be necessary to restructure finances immediately. Being able to completely own one’s home immediately assures an easy transfer of assets. Additionally, in many states, a house owned by a married couple, where one partner dies, is not considered an addition of property to the surviving owner, so no taxes are assessed to sole ownership.

tell him to change the will that if in the event you both are deceased, then the house goes to her. It's just stupid to leave half the house to his daughter. that's like leaving half the family pet to her too. tell him to get his head out of his ***, and leave it to you

it depends. If the house is in yours and his name then she would have to negotiate with you. But if it is only in his name then you would have to sell the house and split the money or one person would have to buy the other persons half . You need to cunsult a lawyer if you are that concerned about it.

each state has it s own laws pertaining to wills however most states will not force the survivor to sell his or her share to appease the recipient of the one half will, and if it is agreed the survivor will receive compensation for their inconvenience, expense etc, which in most cases is most favorable, only a few states still have laws to force the survivor to sell period,

You need to speak to a local lawyer to whom you can show your deed, your wills, & who is familiar with the laws of your state regarding titles to real estate, wills, etc.

The lay advice people give here is more often wrong than not.

if he leaves her 1/2 of the house on the will once he dies , unless specified otherwise, that part of the house will go to her.

She will have half when he dies. It will be half hers and half yours. If that is what he puts in the will.