Debbie Reynolds, Carrie Fisher Will Rest Together Forever at Forrest Lawn

Carrier Fisher and Debbie Reynolds will be buried side by side at Forest Lawn in Burbank ... TMZ has learned.

We're told there will be a joint funeral early next week for mother/daughter. We're told the family chose Forest Lawn because Debbie loved Liberace and the family felt she'd want to be near him. The funeral will be fairly small ... for family and very close friends.

The family had plots at Hollywood Forever cemetery near Paramount Studios and the family even scoped it out Thursday, but ultimately decided on buying plots at Forest Lawn.

We're also told there will be a memorial for the public but so far, no date. Carrie's daughter Billie is having a very hard time and they don't want to overload her with plans.