You say you are bitstreaming but your results are what can occur if you are not, so first please double check. If you are properly bitstreaming, Audio Path will indicate "(bitstreaming)" under OUTPUT, and the Audio Path icon will be blue. Google "jriver audio path" if you need help finding it.
Play a surround sound test track that audibly identifies each channel, and play it to ensure you hear every individual channel, through the correct speaker.
Totally not hearing certain sounds can happen if some channels are not passed or reproduced. Movie soundtracks often have more channels than people have physical speakers.
In JRiver DSP studio, if Output Format is enabled with "no upmixing or downmixing" selected, channels will be muted if the number of channels selected is less than the number of channels in the source audio.
Also, changes to Parametric Equalizer or Room Correction can produce the symptoms you describe, of not hearing certain sounds (channels).
The above issues in DSP Studio should not have any effect IF you are correctly bitstreaming.
Finally, your receiver may have channel mapping capabilities, and those might be configured differently per input. Check to ensure these settings are the same for your input for the AppleTV as for the input connected to the PC.
Other receiver settings could also make some sounds more or less audible. These include dynamic range settings, dialogue adjustments, surround fields, and equalizer/room correction settings. Many receivers allow these things to be set differently for each input. All these receiver settings can affect the JRiver sound even if you are bitstreaming. You will need to check.
When you bitstream with JRiver, it outputs the exact same data as a standalone bluray player. I don't know about MRMC on AppleTV. For all I know, you could have some "enhancement" turned on there that is altering the sound it outputs.
I had a problem just like yours long ago, and it was due to some obscure receiver setting.