WoW! Very nice combo of land and water. What sort of critters are you going to add to this? I really like the back "rock" wall. Where did you find that?
Those actually come with most Exo-Terra vivariums; it is made of foam.
As far as the main topic here and the wet soil issue; it looks like your "water table" is too high. The water will wick into the soil if the soil area is not high enough above the water, and capillary action will draw the water surprisingly high into whatever gravel/drainage material you are using, which then causes the wicking.
Because of this, many people who keep vivaria with a larger water section (for amphibians, vampire crabs, etc.) either keep the water very shallow, have a relatively tall tank (which allows them to have deeper water), or stick to epiphytic plants or species that can tolerate waterlogged roots.
If you really like your water area and you do not wish to change it, you will have to change the plants you have in the soil to species that are more easily able to cope with waterlogged soil.
Cryptocoryne sp. will work well for this; many of the plants in the genus grow in streambanks and other areas where they are only submerged for part of the year; they tolerate being submerged permanently, but they can also be grown in wet soil if the humidity is high enough. If you can find them, plants from the genus Lagenandra work well for this too, and most of the aquarium mosses and liverworts will take off on wet soil.
Finally, I don't know what kind of bromeliads those are, but if they aren't terrestrial, the wet soil will probably kill them. When it comes to vivaria/paludaria, if you want epiphytes, the best way to grow them is with a background that can support them. I'd suggest looking into a tree fern or cork bark background, because (with a drip line to provide moisture where needed) you can grow all kinds of epiphytic things more easily on a background made of organic material.