How to safely build a hybrid battery module?
If you connect a car battery to an uncharged supercap bank, then a very high and damaging current could flow. The trick is to bring them to same voltage before connecting them. Use a resistor to limit the current flow, a headlamp bulb would be ideal, as it's rated for the voltage and dissipates power easily.

Once they are at the same voltage (or very nearly so), connect them directly in parallel. Then you can use the parallel combination as you would a more powerful battery.