General

Your sentence is correct. Since your friend's structure on their sentence is weird.

[quote=hyperfire7]"I went to the mountain with a Japanese man and woman"
Nihonjin no otoko to ona to isshoude yama ni itta.[/quote]

this brah mirin

yours seems correct.
for your friend's translation, -wo is an object marker, so it's incorrect. replace it with particle -ha (subject marker)

[quote=QuackOutLoud]watashi wa nihonjin no otoko no hito to onna no hito to yama ni ikimash""ita

Your translation makes it sound like you [i]are[/i] Japanese man and woman, which is a little strange.

watashi to nihonjin no otoko no hito to onna no hito o yama ni ikimash(what the fudge)ita.

Your friend's sentence makes more sense to me, although l have a feeling 'o yama ni ikimash""ita' is not the right way to say it.
l am personally literally up to paste tense in Japanese class myself and we're learning it right now, so l can't guaranteed this is correct.[/quote]

These are the examples that the professor gave us:
meari-san wa suu-san to kankoku ni ikimasu. It means: mary will go to Korea with Sue (as in together).
and the other one is:
meari-san to suu-san wa kankoku ni ikimasu. It means: mary and sue will go to Korea (separately, not together at the same time).
That's why I thought that it should be: watashi wa otoko no hito to onna no hito to yama ni ikimash(censored)ita.

watashi wa nihonjin no otoko no hito to onna no hito to yama ni ikimash""ita

Your translation makes it sound like you [i]are[/i] Japanese man and woman, which is a little strange.

watashi to nihonjin no otoko no hito to onna no hito o yama ni ikimash(what the fudge)ita.

Your friend's sentence makes more sense to me, although l have a feeling 'o yama ni ikimash""ita' is not the right way to say it.
l am personally literally up to paste tense in Japanese class myself and we're learning it right now, so l can't guaranteed this is correct.

both are correct, but your friends one is better. My japanese teacher said that using "to" after "watashi" emphasizes and lets the listener know that you went together. So I'd say use your friends once.

"I went to the mountain with a Japanese man and woman"
Nihonjin no otoko to ona to isshoude yama ni itta.

@HolyDragon: Thank you. I guess I got that part right....and now the rest of the sentence </3

[quote=Rann]There's an example in the textbook: watashi wa suu-san to kankoku ni ikimash(censored)ita which means I went to Korea with Sue (together). On the other hand, watashi to suu-san wa kankou ni ikimash(censored)ita which means Sue and I went to Korea (separately, not together). o.o[/quote]

I got
"Watashi wa nihonjindansei to josei to yama ikimash(censored)ita."
from google translate so yours is right with the wa.

watashi wa kawaii desu emoji

[quote=HolyDragon]I don't know Japanese but doesn't "watashi wa nihonjin" mean I am Japanese-person and "watashi to nihonjin no otoko" mean I, and Japanese man...[/quote]

There's an example in the textbook: watashi wa suu-san to kankoku ni ikimash(censored)ita which means I went to Korea with Sue (together). On the other hand, watashi to suu-san wa kankou ni ikimash(censored)ita which means Sue and I went to Korea (separately, not together). o.o

watashi wa nihonjin no otoko no hito to onna no hito to yama ni ikimash carrot.
Duh

I don't know Japanese but doesn't "watashi wa nihonjin" mean I am Japanese-person and "watashi to nihonjin no otoko" mean I, and Japanese man...