Is it permissible to give a continuous charity (Sadaqah Jariyah) on behalf of both my father and my mother with the same amount that I intended for my father after his death, and is it permissible for this charity to be for a cancer treatment hospital?

There is no harm in including the mother with the father in the reward of charity. In fact, the mother is more deserving of kindness. Dedicating the reward of charity to more than one deceased person is permissible. Giving charity to a cancer treatment hospital is a good deed, and it is preferable that the hospitals be in a Muslim country and that the benefit accrue to the poor.