If his name is still on mortgage....

I am looking for some clarification. Something mediator said today.... If i trade my share of his pension for his share of the equity in the house but his name remains on the mortgage ( he will pay me child maintenance & probably some spousal maintenance until youngest starts full time education) but in effect I suppose I would physically be paying mortgage from the "income" of benefits & maintenance initially - does that mean that the house is effectively mine? does he have any further claim on the property? Would he still have to pay for life insurance to cover the mortgage if he died? Obviously I would be unable to move from the property until I could raise a large enough mortgage on my own or had sufficient equity or rented (this will not be in the near future)- I wouldn't need to have his permission to sell would I? Hope someone can clarify this issue either from own experience or that they are in the know! Thank you