Unless you purchase a third device as an HDMI switcher, your best bet is the use the other connectors on your TV. For example, if both your TV and cable box have component connectors, you could free the HDMI for your video player. Although your video player may have component connections, some protected-movies will be limited to 1080i via component.
Different markets (regions) have different cable boxes. You'd have to research which boxes in your market support HDMI-In. Go to the following link, enter your Zip and research only the boxes you need, such as with or without DVR service:
www.cox.com/.../identifying-your-cox-digital-receiver.html
if you don't want to research, call your Cox Store for your needs.
Manufacturers (Cisco, Scientific Atlanta, Arris) make the same box for various providers (Cox, Verizon, Comcast). The provider determines if HDMI-In will be active or not. If yours is inactive, it'll stay inactive.
I think you mean HDMI passthrough (Pass-Through).