You have my very sincere sympathy; I think no matter how old you are when it happens, you're never really prepared for it. It's an admittedly hackneyed observation, but a true one, that losing a parent is one of those milestones in life that function as forcible reminders that one is no longer a child (in some strange way, almost more than becoming a parent).
My own dad just passed away, after a short and sudden illness, in February, and I'm also struggling with the difficulty and strangeness of coming to terms with the fact that I am no longer one of those lucky people with both parents living. A wise friend who has lost both her parents advised me to put away the idea of "getting back to normal," since they're never going to, and to think instead of "resetting" or redefining the parameters of what constitutes "normal" now.
In any case, please accept my best wishes for you and your family, and for your collective peace of mind at this very challenging time.