Mice do have backbones. All mice are vertebrates, a group of animals that have a long nerve cord running down their backs which is protected by cartilage and bone. Mice are even use as model organisms by scientists studying vertebrate genes.
Mice have a basic body plan that is very similar to that of many other animals in the vertebrate group. They have internal skeletons, a distinct head and tail region, four limbs and jaws. While not all vertebrates have jaws or limbs, the majority of animals living on land do. The backbone or spine of mice is similar enough to the backbone of humans that the mouse spine is heavily researched for medical applications to humans.