The only ways to get invulnerable in DS2 are:
- rolling, you get more iframes the more agility you have. Iframes are only at the very beginning.
- critical strikes (usually from backstabbing or riposting after a shield parry). You're invulnerable the whole animation, but you can get hit right after it finishes so be careful.
- getting knocked down by an attack, usually something that overpowers your poise by a LOT. Same as above, you're invulnerable the whole animation. Don't swing at knocked down enemies until they start their getting up animation!
In DaS1 you were also invulnerable when entering fog gates, but that's no longer the case in DaS2.
Edit: to answer your last question, using healing items or spells not only does not make you invulnerable, it actually enrages mobs to come at you and stop you! Plan healing for when they're out of stamina or you'll probably die.