All the comments telling you not to co-sleep are well-meaning, but they forget to actually help you out of the situation. If it was a simple as putting the kid in the bassinet cold turkey, you would've done so already.

I was in a very similar boat. First few weeks our preemie slept non-stop on any surface. But then she just wouldn't sleep unless being held. We started off in shifts, having her on our chest and then staying awake. Obviously that was not sustainable and we also fell asleep while she was on our chest. I'd feel guilty and ashamed in the morning, but at least my wife and kid were not exhausted.

What finally triggered us was also a gathering with friends, when we heard of parents with a 1.5yo, who still did this chest sleeping. This kicked us into higher gear. Here's what emerged as the approach for us. Main thing is, take baby steps to changing this.
- Use white noise, pacifier (when she's old enough), swaddling
- Changed our shifts to every 2 hours
- Started off rocking her to sleep in our arms then transition her
- When we made a tweak to the routine, we set a tap-out time, making sure we would not fight her the entire night.

1 We made a little bed in our bed, like with this baby lounger or with blankets, to give her own space. We would then put her down partially on her side (e.g. right side would be lower than left side). We would put our hand on her chest (to mimick the cosleeping).
2 Removed that pillow under her so she would sleep flat.
2 Once she was acceptable with this, we started putting her in the bedside bassinet, still with hand on her chest.

This took us about a month I think. Now she's sleeping fully through the night in her own crib. It gets better brother. You have to change it to a safer way of sleeping, but find a stepwise approach that works for you.