Why do my interior lights get brighter when I shut off my headlights?

It sounds like you need a new battery, but stop guessing and have the battery tested. Have the charging system tested at the same time. Most auto parts stores will do this free, or you could just go to a mechanic.

I've had more than one OEM battery (from Ford) to fail at the three year mark.

Three to four years is what you can expect from the average battery in some climates. Get the battery tested and you will know for sure.

Battery, generation system or a high resistance connection.

Get your battery checked to start. Some auto parts(chains) do it for free.

I don't kknow exactly how it works but if you turn on your headlights in the daytime, the interir lights are dimmer. However at night they show up brighter. Are you talking about daytime?

If you are talking about your dash and radio lights they should dim when you turn on your headlights, if your dome lights dim you have a charging system or battery problem.

maybe your pupils dilate? heehee

To simply answer your question, the interior lights dim because the headlights cause a greater load on the weakly charged battery. This causes the the battery voltage to drop down. The more load you add to the battery the more the dimming will occur.

You need to have the charging system checked out to make sure it is suppling the proper amount of charging current under high load. The fact that you needed to get a jump start means something is wrong, unless you left something on while away from the car. Winter is here and you don't want battery problems. The trouble may just be a loose belt or damaged alternator. A load test will tell the story.