I bought a Payday 2 DLC pack, but I don't see anything in my inventory.

DLC in Payday 2 works as follows:

For masks, many of them are part of the card drop loot pool, while some are awarded for completing certain achievements.

Weapons are locked based on level, so please be sure that you are at or beyond the required level to use the weapon in question.

Weapon modifications, like masks, are generally part of the card drop loot pool, while some are awarded for completing certain achievements.