No the Pokemon have to be in the same evolution line or be a ditto. So if you wanted a Eevee with a Hidden Ability you have to breed it with another Eevee or a Eeveelution.
The most notable change is that Hidden Abilities, which previous required you to have the mother with the Hidden Ability, can now be bred without the mother having it. If the father has got the Hidden Ability, there is a small chance that the offspring will also have their Hidden Ability. However, this only works if you are breeding with a Pokémon in the same evolution chain, or a Ditto. This is even more useful considering Hidden Abilities are more easily found via Hordes and Friend Safari.