In real life I think police are taught to angle their car to a threat which allows them to put the engine block in between them and potential bullets.
Paneling, such as car doors, are not a reliable shield even to ordinary bullets. That only works in the movies.
It is possible to reinforce doors, but is probably outside the budget of most departments.
The following video shows a guy shooting a 9mm and .40 into a stacked backhatch and hood. Eight out of ten bullets go completely through both: https://www.youtube.com/watch?v=0k5OVEx7YVY
And here is a video of an AR15 shooting through both doors of a car: https://www.youtube.com/watch?v=T2OuTY5JuCk