Say I have an Olivia, Mobilized for War on the field, who has this ability:
Whenever another creature enters the battlefield under your control, you may discard a card. If you do, put a +1/+1 counter on that creature, it gains haste until end of turn, and it becomes a Vampire in addition to its other types.
I play a Werewolf and discard a card to pay for Olivia's ability. The Werewolf is also a Vampire now.
A turn passes without anybody playing spells, so the Werewolf transforms. Is it still a Vampire? Or is it only the subtypes written on the card's new face?