Unfortunately, I would not give a dime on anything which a call center agent tells you now or in a week from now. On the other hand, legally, you don't have too many options unless you did not just purchase a ticket from their website but it would be part of a packaged holiday. In case of packaged holidays there is a mandatory insurance against bankruptcy at least in Germany.
Your problem is: AirBerlin may operate your flight or they may not. You will know once you've arrived at your final destination. Given their personnel situation (which is unlikely to improve now and has been bad already) it will be enough if they cannot find a crew on the day you plan to travel.
On the other hand, you don't have any chance right now IMHO to have your tickets refunded and book with a different airline. The only bet on the future you could make is to try and buy a refundable ticket with another airline now (maybe for a day later) and give it back if AirBerlin will fly.
Last chance: Check the credit card you possibly used to pay for the flight. Some cards (especially and "Silver" and "Gold" cards come with all kinds of insurances. Not sure if bankruptcy of an airline is one of them, but it may be worth checking.)
But please also note that all those insurances would if at all only make sure you either get your money back, but you will still not travel then. At least not at the insurance's expenses. Only if there would be such an insurance and you made it to your destination but your flight back home doesn't take place the insurance would pay for suitable means to get you back home, but that would be all. They will never pay the difference to a more expensive ticket if you haven't started the trip yet.