I'm confused because I know German does not have Progressive Tenses as English does. So how do you get around the "-ing" part?
You can use the normal forms as "als es passierte" expresses clearly enough that a new event happens during the action described before.
- Ich war mit dem Auto unterwegs, als es passierte.
Added:Sometimes it takes a bit longer to find an appropriate answer. English has the habit to describe ongoing actions by using the continuous forms and this is done very accurately. German mostly doesn't express ongoing action explicitly with special forms. In the above example both aspects (ongoing aspect and aspect of a new interfering event are implicitily indicated by the contents of main sentence and subsentence.
- Ich war mit dem Auto unterwegs
Logically this can only be an ongoing action whether you express the ongoing aspect explicitly or not.
- als es passierte
The content of this subsentence can only be interpreted as a new interfering event.
I can imagine that it must be a new experience for English speaking persons learning German that it is not necessary to state ongoing actions explicitly and that the content of two clauses indicates clearly enough that one action is ongoing and the other one is interrupting.
I hope I got across what I meant to say. Not so easy to express such subtleties in a foreign language.