The Dish Network User's Resource
You can mount a DirecTV LNB on a Dish Network dish, but the reverse is not easily done. DirecTV LNBs have a rectangular mount while Dish LNBs are D-shaped and won't fit on the rectangular arm. If you want to use a DirecTV LNB as part of your Dish system, there's no good reason why you can't. DirecTV LNBs are equivalent to Dish legacy, so can only be used with legacy switches, not DishPro. Do not use the “Sat C” LNB or anything with an integrated switch.
But if you mean to receive both Dish Network and DirecTV services with the same LNBs from one or more dishes, it's a more complicated question. With the right equipment, you apparently can. See: http://www.techweenies.com/dss-1.shtml for diagrams and photos of several configurations that are possible.