Remove "and I" to figure out whether to use He or Him, and remove "He and" to figure out when to use "& I" or "& me".
It's destination is not a house party where everyone was waiting for you're arrival.
All seriousness though—this pedant appreciates you giving me an English grammar rule to brush up on. My pronoun work has been strictly en el español of late.
AFAIK, "Him" has been the accusative (subject) form since at least Old English. https://www.etymonline.com/word/him
ETA: I generally don't bother "correcting" the grammar "mistakes" that native speakers make (like "My dad and me did X"); but if I think it's pretty clearly a non-native speaker, I'll correct them, because that's what I would want someone to do for me if I were speaking in their language.