If I fly both Part 135 and Part 91 in a 24 hr period, which regulations apply?
Part 91 contains the General Operating and Flight Rules. These rules apply to almost every civil flight within the USA. 

Part 135 contains the Operating Requirements for Commuter and on-demand operations and the rules governing persons on board such aircraft.

So when you fly the "Part 91 flight", you follow the regulations of Part 91. 

When you fly the "Part 135 flight", you follow the regulations of both Part 91 and Part 135. If Part 135 is more strict in some regard, the more stricter rule of 135 applies.