Fresh Supply is using Nightdive Studios own Kex engine. Which you can consider it to be similar to GZDoom/Raze like to keep it simple. But it is proprietary and not open source.

Fresh Supply can also use the CD tracks if desired. Change in the Audio config inside game. But as to MIDI....

Fresh Supply is using FluidSynth for MIDI replication. Just like back in the day with MIDI devices, the samples / sound fonts / hardware itself all could sound different than each other. SB Midi not the same as Roland GS which is not the same as Roland MT32 even, and every manufacturer of Sound cards and chips sounded different and were of varying qualities. Some notoriously bad or just wrong samples (not MT32 or General MIDI compatible), some just slightly off due to missing some small thing. Repeat for all the software MIDI stuff like fluidsynth. Nice thing about fluidsynth is you can change the "sample/soundfont". How to do that in Fresh Supply.... will check in a moment, but it comes with the TimGM6mb.sf2 Sound Font. Which seems to be a small GM (general MIDI) SoundFont from older MuseScore version. But not used in newer versions? I am not a MIDI/SoundFont expert. I kind of like the original SB Pro adlib/FM myself over MIDI for old DOS games.

Okay, in C:\Users\<yourusername>\AppData\Roaming\Nightdive Studios\Blood EX\ there should be a file called kexengine.cfg. In there should be a line: seta snd_soundfontfile "TimGM6mb.SF2".
Download whatever soundfont pleases your earballs, put in the Fresh Supply main folder. Change that line in the kexengine.cfg to same name as the sf2 file you just put there, and see if your MIDI has changed properly to the new SoundFont.
Sadly, they did not seem to put this into their user interface menu directly.
And, there is a chance, even though it gets put in the cfg file, they may not accept other sf2 files at all and just overwrite that config setting with default. I have not tested this to see.

It as Zandrag stated uses KEX which is a closed sourced engine, I would suggest that you use the OUWB download and use NBlood or NotBlood that goes back to the build engine instead of the weird chimera that is KEX, while good for other games, its code for the build engine isnt as good.