The allowance to which you refer is the Residence Nil Rate Band (RNRB) – an extra slice of Inheritance Tax (IHT) exemption that can be claimed when you pass your home or its value on to direct descendants (children and grandchildren).
The good news is that the RNRB does apply to stepchildren and, in fact, also to adopted or fostered children.
It can also apply to your direct descendants’ spouses or civil partners, but if the direct descendant has died, their spouse/civil partner must not have remarried or entered a civil partnership.
Both the standard Nil Rate Band and the Residence Nil Rate Band can be passed to a surviving spouse or civil partner if it is unused on the first partner’s death.