Yes, we have a valid will, stating burial for me certainly. DH said the same originally, but has perhaps changed his mind to cremation and his ashes spread at sea. Better check that while we are both fit and well!
Decided long ago, that if one of us dies abroad then burial takes place there, as neither of us see the point of paying transport home. I have stipulated a requiem mass in my parish church irrespective of where I die and am buried.
If a cardboard coffin is not legal where you are, you could ask for a Jewish coffin. They are made of unvarnished (unpainted) boards as everyone is equal in death and don't have any religious symbols on them.
Do check the legal aspects of your wishes. Here in Denmark it is illegal to be buried or cremated without a coffin, and you need special permission, which is rarely granted, to be buried on your own ground. I should think a grave in the garden would make selling a property nearly impossible.
I know we all have to die, but I would not be comfortable with a human being buried in my garden! Cats and dogs, yes, but somebodies DH or DW or baby, no.