Help please - can't get my head round this, despite having looked in Act, Regs, DMG and CPAG handbook... Couple, both under 18, with a baby. He has claimed JSA (IB) for both; Jobcentre Plus told him both of them must register for training/work and whichever is offered either first, must take it up leaving the other to look after the baby. Can this be right?

They fall into the catergory of under 18s who can claim JSA under normal rules at any time. They will only get the £65.30 rate of personal allowance though.
Therefore there is no requirement for registration with Connexions, as there would be in a 'severe hardship' case.
They are not a joint claim couple ( and both required to sign on) as they are under 18 and also because the partner is responsible for a child.
I'm sure what you have been told is wrong.