the three bloodlines or in your sentence:
fifteen hundred troops joined the ~joint armies of the three bloodlines~
If I read the OP correctly, he is trying to convey some of the "sense of self" the "peoples" have while referring to them.(I infer that from his refering to nationalities as peoples as well as his desire to stay clear of the word 'combined')
If I read right, he wants to use mostly modern language, but convey sensibilities of self-perception of the people involved. Quoting OP: but I'm staying away from present-day terminology in sciences of all types.
The terms nation and especially "multinational" carry with them so much of a anthropological self-awareness and political science uses that even if a dictionary definition works, the taste of the words misses a chance to contrast these groups with our notion of groups in the west and in modern times.
The word Bloodlines, I think, captures what a people was to themselves at that time. Even more than the already strong "shared history" their ancestry was eternally alive: Father to son to grandson, brother to cousin to cousin in a spiritual sense. They had more yeasty sense of "our people" than our sense of individuals or distinct generations.
I think this kinship-centric sense of people is particularly strong in the middle-east. (I read the OPs desire for words particularly apt to the middle east by naming of the groups he did)
I also see why the OP might avoid "combined" as that does imply mixing and de-emphasizes separate entities fighting side by side. "United" might be better but that carries some sense of meeting of the minds.
To me, "Joint" would emphasize separate autonomous entities with links created for a particular situation.
"Force" also seems a bit modern to me.. I'd choose "armies", also plural emphasizing their separateness.
"Joint armies of the three bloodlines" seems set apart from modern references yet uses modern words joined together.