Hi, i have been searching for this too. Here is how as vBulletin forum admin you can show child forums (or subforums) on forum homepage.

Go to vbulletin administration, then click Options, vBulletin Options, Forum Listings Display Options
Then on the top you will find 3 options of Forum/subforum depth. I had default: 2,2,0. Do it like 2,1,1 and save.