I am laying tile in my living room. I have a sliding door to the balcony which have a door casing made of two stacking 2x4s. Previously it was wrapped by carpet as a stair. As shown in picture the people who did the carpet used a piece of drywall to match the thickness of surrounding walls and then just stapled the carpet to it. The drywall degraded due to moisture and the condensation water dropped from the sliding doors.
What are my options to deal with this step? I could attach 1/2 MDF to both top and side then paint them, then attach baseboard to transition to the tiles, but I worry about the moisture.