OK a policy change occurred. I worked at one in the early 1980's.
Depending on your states contribution your grave is paid for as is opening and closing and the headstone. The V.A. provides this. The veterans spouse {one only} is also eligible as are any minor dependents for burial there. In my state for my wife the vault, opening and closing cost about $900. When I pass the cost for me besides the funeral home expense will be $0. The vet is buried no cost. When you consider you can quickly be out $6000 to $10,000 for two plots and burial cost paid to a cemetery alone besides funeral home expenses this is well worth considering.
The veteran and one spouse share one common grave. The first to die is buried about 7-8 ft deep and when the other passes that spouse is placed on top at about 5-6 ft deep. They will also share the same head stone. If one spouse dies and the other is living the dead spouses stone faces forward until the veteran spouse dies. At that point a new headstone is ordered and the veteran's name goes in front and the spouse in back.
Do you know where your DD-214 is? The funeral director will need this to present to the cemetery administrator. For WW2 vets it looks different than the more modern ones. The WW2 era DD-214 is black and a lot smaller in size. You will need it though and family members need to know where to find it.
Most veterans are unaware they have this benefit but most vets do have it. The change in GI Bills back in the 1970's didn't change this part.