From what you stated, it sounded as if the voltages your external devices expected were negative. I would make certain that is correct before connecting your device. If that is really true, then you would simply need to invert the polarity when connecting to your 6115 board. You could do this by connecting the positive terminal on your external device to the DGND pin on the 6115, and the negative terminal on your external device to the corresponding digital line on the 6115.
Alternatively, you could connect the +5V line on the 6115 to the positive side of the external device, and the respective digital lines to the negative side. If you used that method, then you would also need to invert all of the output logic in your application.
Other than the possible inversion, the specified voltage ranges of the 6115 should work fine. What type of terminals does your external device provide you with? Hopefully you are given a positive and a negative terminal for each line. If you are not, then some other method for interfacing these two devices would have to be used.
If you discover that the voltages specified for your device are not actually negative, then you can simply wire it up the normal way.
I hope this has helped,
Jason