Where did you read that both parents can be paid at the same time?
Hmmm interesting- I assume that given overall the pay has to be reduced you could try and argue with them to still be paid in that month but your overall pay would stop a month earlier? Is he getting the occupational pay in that period or statutory? Does the calculation work out overall so you get your occupational pay later/what is your partner getting in that month? By the sounds of it the overall amount you are entitled to should stay the same it is just distributed differently. It is confusing though!
This unfortunately is how I understand it - you are sharing the leave and pay - so whilst both of you can be off - they only pay one of you and the time is then also deducted from your total allowance. Unless your partner gets separate enhanced paternity leave himself I would assume only one of you can be paid via shared leave at a time! Whether he gets statutory or occupational pay I think does vary depending on which NHS contract you are on.