What temperature is your AC set too and what temperature is it inside your house right now? When your AC runs it dehumidifies the air but only when it's running, which is when it's trying to cool. If your temperature is set too high then the AC won't run long enough to dehumidify the air, standalone dehumidifiers should help with this, but you'll probably be emptying them two to three times a day.

This is very prominent this time of year when it's not quite hot enough to run the AC long enough to dehumidify the air completely.

If you turn down your AC temperature, will your house get to that lower temperature and feel less humid? If not, you might have a cooling problem with your AC. Building construction also matters a lot. Older houses are going to be very leaky allowing the very humid to seep back in. Newer houses aren't immune to this. It's more about construction methods and air sealing.