Homeowners Insurance will usually cover black mold and mold damage that occurred due to a natural disaster letting water get into your house such as a roof being torn up or shingles coming off etc.
If the mold was caused by a preventable leak such as a water pipe leak etc then Homeowners Insurance will not cover the cost to repair the black mold or any mold and that cost would come out of the homeowners pocket to repair the mold damage.