Voltage drop across each diode and current drawn from battery
Both diodes are opposing therefore they block current in either direction therefore neither diode is forward biased. You do actually need current to flow to get any meaningful forward bias situation.

Of course there might be leakage currents (25 nA for the 1N4148 at 25 volt reverse voltage) but these are so small that the relevance of considering if one or the other diode was forward biased is lost. For instance if you looked at the 1N4148 forward characteristic you'd see something like this: -



At 100 uA, the forward voltage is about 0.5 volts and the voltage will drop at a rate of about 0.1 volt for each decade reduction in current hence, with 0.4 volts applied, I would expect the current to be 10 uA. For 100 nA I would expact the terminal voltage to be only 0.2 volts and 0.1 volts at 10 nA.