To answer your question, you should be able to use 3 simultaneous independent displays with the back panel graphics connectors on the board (DVI, HDMI, and Display). Both processor and motherboard support this configuration so there should be no problem at all.
I would like this to be true, but I'm skeptical given the documentation.
From the DH77EB spec: "If using a processor with integrated graphics, the board will support only two of the integrated graphics interfaces simultaneously: DisplayPort, DVI-I, HDMI.
There's also this FAQ: "What three independent display configurations are supported?"
Can anyone confirm whether this board is an exception to the rule? And if so, what are other Intel boards supporting triple-display with the Ivy Bridge graphics subsystem?