No, it is not safe. Storing loose batteries with metal objects like drill bits and screws is a major short-circuit risk.
The battery terminals can connect with these metal items. If they bridge the positive and negative terminals, it can generate enough heat to cause burns or start a fire.
You should store the battery pack by itself, or in its original compartment in the kit box where it is isolated. When transporting individual packs, ensure the terminals are protected. You can use the plastic terminal cover that sometimes comes with new packs, or place a bit of electrical tape over the contacts.
There is no safe alternative to keeping batteries and metal objects separate. Also, do not throw spent batteries in the trash. Recycle them at an authorized DeWalt center or retailer.