Our home is in my name and my daughter's name,the mortgage is in only her name. She has passed away,I have been paying the mortgage the whole time,is the home still mine?

How was the deed titled? If it was titled Joint Tenants with Rights of Survivorship then yes you own the house subject to the mortgage. You can take a copy of the birth certificate to the Registrar of Deeds and have the house put in your own name.

If it was not Right of Survivorship, then her half goes to her estate and will be distributed according to her will of your area's laws of inheritance.

Was your name added to the deed after the mortgage was written? If so, you may have issues with the mortgage's due on sale clause.

Note: any question on law needs to include your general locale as laws vary by area.

Agree with Scott, you obviously own your 1/2. but her 1/2 is up to the wording of the deed, and/or her estate