I'm testing monstera adonsonii and syngoniums in my new tank right now and they seem to be doing well, the adonsonii doesn't like being relocated and is losing leaves near the water level but new growth is constant and the syngonium is loving the aquatic life. A preface to the following information: plant experience I have but fish I do not.
Virtually any epiphytic plant should do well with their feet wet. A method one could use is using a hanging basket of sorts on the tank to partially submerge the plant and have the roots reach towards the bottom and eventually dive into the substrate. Another method is mounting: use coated wire, don't want minerals contamination on the roots or in the tank or rust, and bind the root ball to a piece of drift wood or a stump, space provided, and have a more natural look instead of the basket. Finally, an option is to have a taller plant, such as an anthurium, which already has the leaves well above the water line to be partially submerged as well.
The only problems with most of these use cases is: a lid can't really be used for the tanks, this means either larger tanks with lower water levels to have the "epic jungle feel" or to have a hovering lid of sorts which allows the plants to creep out the side as they grow larger. Of course this depends on fish and other configuration issues as well, but my 10 gallon rimless housing neon tetras, otocinclus and ghost shrimp haven't had an incident thus far. Benefits of mid to bottom feeders I imagine.
Once I feel comfortable with this 10 gallon being stable and functional I plan on shifting towards a 45 gallon and doing much larger plants with driftwood, stumps and maybe expanding foam. Plant selection thus far include: anthurium, spathiphyllum and chlorophytum. I will be testing dieffenbachia, philodendrons and calathea to see how they play in wet feet configurations.
If any of you would like to keep an orchid near the tank simply hang it above your tank with a few roots in the water or mount it on the rim somehow and watch them thrive!