Ive always used these with a different soundcard feeding the mixer as analogue audio (this can however be on the same computer), and the in built soundcard being used for the streaming.
Firstly all make sure you have got the Behringer ASIO driver from their website correctly installed. You may have to unplug the mixer USB, uninstall old versions and restart the computer without the mixer plugged in, then reinstall the new version, reconnect the USB when the install software instructs you, and reboot the computer once more.
If this is computer is a laptop or gets used for other stuff, take care to mark or note which USB port the behringer is connected to as the driver only works correctly on this port.
use this newer version of Edcast with the ASIO support
https://code.google.com/p/edcast-reborn/downloads/list
On Edcast, set your stream source to be the BEHRINGER USB AUDIO and make sure ASIO settings (double click on the ASIO icon) are 44100 16 bit (others do not sound good).
for all your other playout software, set the default output to be the other soundcard on the computer (you might want to do this in Windows control panel). Connect this to a stereo input with a cable - you may need a small stereo trafo (audio transformer) to remove noise from the computer power supply. I am not sure what country you are in otherwise I would have suggested one (in the UK you can get them for £6).
You can then use the stereo channel and the mic faders as you would any other mixer.
Be careful about levels; although the analogue side of these mixers will go over 0dBU and there is some headroom, if the digital soundcard gets sent too strong a signal it will be over 0dBFS and the sound will be clipped.
It took me a while to understand this when I got back into music a few years ago (as I am old and started off in analogue days).
The Peak meter on Edcast is what is actually going to your stream. You can also use these meters (most are free, but the €14 one is worth the money) to get a larger display of the levels.
Audio Level Meter
if your computer can drive an extra monitor you can put all the streaming / level displays onto this and use the main one for the playout.