The president still sometimes mentions his son in the present tense in private discussions, according to people who have spoken with him. He carries his son’s rosary beads with him, once holding them aloft during a virtual meeting at the White House this spring with the president of Mexico. Several people close to Mr. Biden conceded that he sometimes does not always seem to be aware that broaching his own loss can make others uncomfortable.

But, of his rocky reception with some families at Dover, Ms. Murray said, “I’m sure he understands the reaction he got better than a lot of people.”…

Mr. Biden’s advisers privately acknowledge that not everyone responds in the same way, and he does not always adjust his approach depending on the audience.

Mr. Schmitz, the father of the young Marine who died in Afghanistan, said that in the past week, he had looked for opportunities to tell anyone who would listen about who his son was. His son Jared, he said, had been proud to be a Marine in a Navy family and had wanted to serve in Afghanistan for a chance to help people there. He wants the world to know his son was a hero.