One big question is do you have mechanical ventilation? If so you might see if it runs continuously or intermittently. Intermittent would generally be best as long as it meets your needs, as you would not be continuously sucking in humid air but that would have to be discussed with a professional with all the information handy.
The first step to lowering indoor humidity levels is reducing interior loads. Run your bath and kitchen exhaust vents (which need to vent outside - no recirculating or dumping in the attic) whenever you cook, take a bath, or shower.
- After you are done cooking you can turn it off within a few minutes.
- As for showers and baths, you should let it run on a timer for 10 to 20 minutes after you are done (yes this even includes cold showers).
How many plants do you have inside? While they are great some push tremendous amounts of water out, so be careful there.
Unfortunately the rest comes from outside and even from us (breathing, sweating, etc...) and either it has to be removed by the AC unit (which should be properly sized and running almost non stop during the hot summer days) or via a dehumidifier.
I do not know what unit you have or how the dehumidifier works with it but you might want to have it checked and make sure it is set to get to the humidity level you want instead of stopping at 50.