How do you get a newborn to sleep on their back & in a bassinet?

We have a one month old who slept great in his bassinet the first two weeks. Now He will only sleep on us, in a swing or in the bouncer. We keep trying to put him down in the bassinet but all he does is scream. If we put him down already asleep then he wakes up within 5 minutes screaming. Needless to say we are averaging 1-3 hours of sleep a night (we take turns sitting up with him) We are exhausted. Any helpful tips to get baby to sleep on his back again and in his bassinet?

We swaddle with a SwaddleMe and use white noise.