Strong Temperature Inversion
If you are okay with messing with the atmosphere you could provide a strong "sunscreen layer" in the upper atmosphere to block the majority of the non-visible light. Imagine something like this, but not as hot and closer to the surface.
A strong temperature inversion like this would create a very hot layer above a much cooler more stable layer, and still conceivably allow you to see. If close enough to the ground, and strong enough, it could prevent most if not all convection processes at surface level where rain forms. The mid-western U.S. has a much smaller and weaker version of this called the "CAP." This hot layer of air from the desert southwest can completely shut down even explosive weather scenarios by acting like a glass ceiling, stopping even a single storm from forming. The upper atmosphere would have storms, but out of reach of the moisture from the oceans. All you need for this to work is to have the temperature increase as you go up in altitude. Since convection requires cooler air for warm air to rise into, this would effectively shut that down.
What it would probably look like:
Since about half of your planet is covered in oceans, there would be still be fog at or around sea level. This is almost unavoidable in any scenario. But at any higher elevations there wouldn't be fog, or even really clouds. Think of the Atacama Desert in Chile. Hundreds of years without rainfall, yet around the ocean there is cactus, and other flora that thrives solely on the fog.
The weather of your upper atmosphere including overcast, broken cloud cover, lightning, or clear skies would appear to slide over an invisible plane, like being underneath a glass coffee table. Your view can change drastically based on the make-up of your atmosphere. The lower and mid atmosphere would nearly always be clear of clouds.
Your planet would be very humid, like the north Persian Gulf in summer, and there would be minimal or no surface wind to change that. That does depend on how warm you need the surface to be though, it could conceivably be near freezing if you want. The important thing is that whatever the surface temperature is, the upper atmosphere would need to be much hotter in proportion. Also the temperature would be a very constant thing even through the day/night cycle as the upper atmosphere would act like a colossal blanket, trapping the heat inside. And strangely, when you hike up in elevation the temperature would always increase as you ascend.
I am not all that familiar with chemistry and the properties of gasses. But you would need a mix of gasses that would block UV radiation, while also blocking and trapping infrared radiation, all without blocking most of the visible light.