Is it permissible to bury Muslim and non-Muslim dead together if they perished and it was not possible to distinguish between them?

It is not permissible to bury a Muslim in a cemetery of disbelievers, nor vice versa, except out of necessity. If it is impossible to distinguish Muslims from disbelievers, then it is permissible to bury them together, because burying Muslims is obligatory, and it cannot be fulfilled in this situation except by burying everyone.