That actually wouldn't be a problem with your camera. If they can see you, your camera is working fine. If you can't see them, it is their camera that isn't working correctly and they need to check.
If it turns out it isn't their camera (which I have to say it really sounds like it is) then I would check your access and/or theirs on whichever app you are using to connect to them with (skype, google, etc.) and see if the settings are blocking you from seeing their camera.
Again, if 'they' can see you, it isn't your camera.