Hi Kate W,
You don't generally have to provide bank statements with Managed Migration. You may hear a lot about UC demanding bank statements at the moment and that is usually to do with the Enhanced or Risk Review Teams and affects people currently receiving UC.
UC Migration has no effect on PIP and you don't need to supply medical evidence. Though you may be asked to, which the DWP has admitted is caused by a " bug " in their IT systems.
You and your husband should receive the carer's element in your joint UC claim. As he is a carer he doesn't have to look for work or do work preparation. Carers Allowance is deducted from UC as with the other means tested Benefits.
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
