Weight painting with multiple objects

I’m rigging a character for the first time and the separate meshes are splitting apart when I move the armature. I know this is a problem with weight painting but I have no clue how to fix it.

Can you join the meshes into a single object? Perhaps only temporarily, in order to weight paint them as a single unit? (All that work on multi-object editing, and one of the best potential use cases, multi-object weight painting, doesn’t work…)