An update.  I tried the configuration you have with two digital monitors one connected to the DVI-I connector and the other to the HDMI.  This configuration works correctly.  The problem is when an analog RGB monitor is attached to the DVI-I connector, using only the analog RGB pins, and if the computer is booted with a digital monitor on the HDMI output, the analog monitor will not be available to Windows.  Since there is no splash screen on either ( the primary is the DVI analog) it seems like the card is choosing the digital output on the DVI-I connector, which is not connected.  Hope this makes sense.

Yes, I am using the primary DVI connector to drive a monior and the HDMI to drive an HD TV.  This works well.  The problem I was having was to use the DVI-I connector to drive an analog monitor.  DVI-I has both digital and analog.  This did not work well if I wanted to drive an HD TV on the HDMI port.  Two digital devices work great.  For information, I tried many different configurations with the HDMI output.  I used HDMI extenders (cat5e), drove a HDMI 2 and 4 way splitter.  Also, a 4X2 matrix switch.  The matrix switch was the only device the port did not like.  I fixed this by placing a HDMI 2 port splitter before the switch and all is well.  So, blame the switch.  I am currently using this computer to drive 6 HDMI LCD displays located through-out a church, streaming announcements.  The switch allows me to stream live video.  The longest distance is about 300 feet, so the HDMI extenders do their job well.  I have limited the video rate to 720P because of the distance.  I will say the computer, with this board works like a champ in this application.