Yes you can crossfire two cards from different brands, but you don't need to for mining.

The cards should perform better if you don't crossfire them.

Be wary about the XFX cards, they are the cards I detest in my mining rigs. My XFX 5850s run much hotter than other brands I have and they were the worst when it came to overclocking. My asus and sapphire cards perform the best. Not sure about HIS, never had one.