You can connect HDMI & DVI if you use the appropriate cable. I suspect that "HDMI/DVI" port is labeled that way for that reason. However, if you use DVI you'll have to provide a separate connection for audio. That HDMI/DVI port may have a setting for use with a separate audio connection that regular HDMI ports wouldn't have. On both of my TVs, that separate connection is a mini-phone jack.
If it's a HDMI connector on the TV and also on the BR player, then a straight HDMI - HDMI cable should be OK. It's only when HDMI - DVI cable is used that separate audio is used and that port has to be configured to use the separate audio. As I mentioned, both of my TVs have that on one of the HDMI ports. In that case, a HDMI - DVI cable is used to connect a DVI device, along with audio cable.
jayoldschool: You need to reread it again. the HDMI/DVI port is the port on the TV and the only thing that mentions DVI It is actually just a HDMI port with the 2 composite audio ports. The HDMI/DVI port works like a normal HDMI port if it is connected to an HDMI device. For example. Blu-ray to TV hooked up using a HDMI to HDMI cable.
It sounds like the only reason DVI is mentioned is due to the audio connectors. When connecting devices with DVI out, a separate audio cable is required. (DVI does not support audio.) When connecting to a device with HDMI out, that should be all that is required.
The DVI & HDMI ports are compatible for the video signal. If you have to connect a DVI device to HDMI, you get a cable with DVI connector on one end and HDMI on the other. However, you'll also need an audio cable and then configure that HDMI port to use the separate audio connection. On the other hand, if you connect a HDMI device to that same port, you do not need a separate audio cable nor do you have to configure for separate audio.
BTW, My Sharp Aquos TV has 6 HDMI ports. Only one of the six can be configured for use with DVI.
Some TVs have this feature while others do not allow for audio unless it's HDMI at both ends, or the DVI at the sending end is a computer which often sends audio out the DVI. Anything that doesn't send audio out the DVI (most STBs, etc) will require that type of input on the TV, along with the analogue audio cables for audio. The TV usually needs to be specially configured in the user menu, but this is all probably described in the operating manual for any TV that has such a feature.