We do not have any DC-coupled design for the DRS4. The reason for that is that for many applications we use SiPMs, which are directly powered through the DRS4 board. Since the bias voltage of ~50V would kill the DRS4, we always go with AC-coupling. 

The reason the DRS4 evaluation board cannot fully capture signals below -0.5V is the fact that the board only has a single +5V power supply and no +-5V power rails. Having an additional -5V power rail would make the evaluation board too bulky and it could not be powered over USB.

In principle you could bias the point after the AC coupling capacitor to +5V, then you can capture up to -5V signals. Add a divider by two to go up to -10V. But then the input protection diodes won't work as it, you would need some fast 5V zener diodes which open for signals below -5V to protect the following circuitry.

Stefan