Descend upon the Sinful

If you have three non-sorcery card types among cards in your graveyard at the time Descend upon the Sinful resolves, you won't get an Angel token. Descend upon the Sinful isn't put into your graveyard until after it's finished resolving.

Because you consider only the characteristics of a double-faced card's front face while it's not on the battlefield, the types of its back face won't be counted for delirium.

The number of card types matters, not the number of cards. For example, Wicker Witch (an artifact creature) along with Catalog (an instant) and Chaplain's Blessing (a sorcery) will enable delirium.