Bethalize, I'm also an extrovert married to an introvert and the mother of a more extreme introvert than his father.
Let him be. If he wanted to come out with you he would. He wants to be alone and process. I understand that you don't want to leave him alone with his grief, but that may be what he needs.
My Husband's father died shortly after we married while my husband was deployed in the Navy and he was not given leave to come home and attend the funeral. His dad had been ill for a while and his passing was not a surprise, when my husband was called in to the XO and given the news, for a second he thought something had happened to ME.
I think while he would have liked to have been given the opportunity to go home and support his mom, the fact that he was able to stay disconnected and deal with it on his own terms gave him greater peace than going home.
Hugs for you and your husband, I'm so sorry for his loss