Given their extraordinary lifespan and cost effectiveness, I expect that lead carbon batteries will be the future technology used in hybrid cars.
Since they are a variant of lead acid batteries, we can expect that whenever they are charged, a small amount of the water in the electrolyte will be electrolyzed,
and split into hydrogen and oxygen.
Normally, such produced gasses are vented to the atmosphere, to prevent them from building up in the battery compartment, and potentially exploding.
I propose designing a battery in which the hydrogen and oxygen produced by electrolysis are vented separately from one another. The oxygen could be vented into the battery compartment or the atmosphere, and the hydrogen would be piped into a small reservoir.
When engine power is needed, we would whatever hydrogen is in this reservoir, in preference to the fuel in the tank.