Gradual Retreat may be worth a try.
Basically you put them in their cot and do whatever you need to do to calm them and get them to sleep, so pat, shush, hold hand, etc.
Night 2 you do the same but reduce the time you are patting, etc but still saty by the cot.
Night 3 try not to pat but if you need to then do, but only for as long as they are crying. As soon as they stop, you stop patting.
Once you can out them in the cot without them screaming you spend the next night sitting next to the cot while they fall asleep.
The next night you move away slightly but stay within sight/arms reach if necessary.
If you can, move away a bit further the next night and each night after move a bit further until you are by the door, then on the landing, then hopefully you can just walk out and they will settle themselves.
It takes a few nights as it's very gently/gently but it's much less traumatic for everyone involved.
When DH did it with ds2 he also used to say Shussssshhhhh every time ds2 started fussing and after a few nights we could shush him from outside the door and he'd settle down again.
If you can hold of a copy of 'The NO Cry Sleep Solution' by Elizabeth Pantley, there is lots of good strategies in there too.
You both have my sympathies, it's an awful phase but it will get better .