Is it possible to Receive benefits at the same time

Both father and mother are equally (or almost equally) eligible for Elterngeld (parenthood support). How much you get depends on the amount your income is reduced by. You should contact your local Elterngeldstelle for the details and how to apply. My experience is that they give good advice through their phone hotline.
Arbeitslosengeld (unemployment benefit) is available for anyone who is looking for a new job, lost the previous one without own fault and paid in long enough. How much you get depends on the amount you previously paid in. For the details contact your local Arbeitsagentur.
One person cannot get Elterngeld and Arbeitslosengeld at the same time, but as far as I know one of you can get one of them, the other one the other - as long as both of you are not working, but one is job-searching.