If you want the Child to be a subclass of parent in db also, you'll need a discriminator column.
If you just want to reuse code then share a mapping base class
public abstract class ParentChildMapping<T> : ClassMapping<T> where T : Parent
{
public ParentChildMapping()
{
// map shared properties here
}
}
public class ParentMapping : ParentChildMapping<Parent>
{
}
public class ChildMapping : ParentChildMapping<Child>
{
public ChildMapping()
{
// map additional properties here
}
}