I know Nazi Germany had both the apolitical Heer and the Nazi SA, but does China have a seperate force which is not part of the Chinese Communist Party?
Nope. The People’s Liberation Army is run by the Communist Party. In practical matters, that doesn’t matter a whit because there isn’t even a pretense here that the government isn’t also run by the Communist Party.
Actually there is a pretense that the People’s Republic of China is not a one-party state. The governing body in China is the Chinese People’s Political Consultative Conference, which is nominally a coalition of nine political parties. Of course, one of these parties is the Communist Party and they outweigh the other eight.
As you note, it’s the Communist Party and not the PCC that runs the military.
What’s it like to be in one of the other 8 parties in China? Similar to being a Jewish politician in Iran, I suppose?
There’s a big meeting once a year where all the parties get together and set policy and make political appointments. Obviously it’s mostly window dressing. The real decisions get made by the Communist Party and the conference just rubber stamps them and maybe gets a few token positions. But it means the Communists can pretend they’re allowing other parties to participate. So if they’re mostly ignored at least it’s done politely.