Try to update any drivers you can, and if it’s hardware issue – did you have similar issues in another games/programs?
You might want to add a more extensive info like DxDiag report, for example, to make it easier to narrow down the source of this problem.
What about your windows sound settings? (it can Mute all sounds if detecting communication activity)
What programs running in background while you play Battle Brothers?
Can you recall any changes preceding this problem, like (un)installing new software, changing or updating something?
Since when did this problem began appearing for you (new patch/update)? Did you play on this same version without experiencing this problem?