Your family liability insurance
If you cause damage to someone else as a pedestrian or cyclist, your family liability insurance (familiale verzekering, covering private civil liability) will in principle pay out. It covers damage that you, your family members or your pets unintentionally cause to third parties in private life.
Your own injuries
Your own injuries or your damaged bicycle are not covered by family liability insurance. For that you need accident insurance or comprehensive bicycle cover.
Behind the wheel
In a car it is different: your third-party car insurance pays for the damage to others, but in the event of serious fault the insurer can reclaim part of it.